高维纵向数据中边际模型和混合效应模型的若干研究
|
摘要
这篇论文致力于对高维纵向数据领域中边际模型和混合效应模型的深入研究以及方法上的延伸。
纵向数据是指对同一个个体或者试验单位在不同时间进行观测而得到的由截面和时间序列相融合的数据。它在心理学、社会学、医学以及生物学等科学领域中经常出现,其最大的特点是其将截面数据和时间序列数据结合在一起,既能分析出观测单元随时间变化的趋势,又能分析出总体的变化趋势。近年来,对纵向数据各种模型的研究引起了国内外统计学家的广泛关注。在本文中,我们主要研究了两类模型：边际模型和混合效应模型,探讨了它们在高维情况下的参数估计和变量选择的问题。
在本文的第二章,对于特殊的广义线性模型Logistic回归模型,我们提出了一种两阶段的收缩估计方法来同时进行变量选择和参数估计,其主要思路是在广义估计方程的非保守向量场内,通过引入一种特殊的加权机制来构造加权最小二乘型的函数,然后利用Zou[104]所提出的自适应性最小绝对缩减和变量选择算子得到回归系数的稀疏估计。我们在维数发散情况下,证明了该收缩估计方法具有Oracle性质,即模型选择过程的相合性和非零参数估计的渐进正态性。同时,我们对参数估计的协方差函数提出了一种相合的三明治估计,并且提出了相合的惩罚二次型准则来应对调整参数的选取。最后,我们讨论了一般广义线性模型下该收缩方法的应用。
随着计算机计算技术和其他现代技术的发展,使得收集和处理海量复杂数据己成为可能,比如利用DNA微阵列技术收集到的基因表达数据。但是,在纵向数据情况下,超高维基因数据的特征选择一直没有得到很好的解决,因此,为了填补这一空白,在本文第三章中我们提出了一种基于广义估计方程的筛选准则,它只须对一二阶矩和工作相关系数矩阵进行假定。不同于文献中已有的筛选方法,该方法无须拟合所有的边际模型或计算配对相关性,它只须通过对估计函数计算一次即可快速完成特征的选择。同时我们还证明了该方法具有稳健性,即使在工作相关系数矩阵错误假定下,仍然具有Sure Screening性质。
本文的第四章是通过对关于癫痫发作次数的某实际数据的观察,提出了广义单指标模型来对数据建模。为了让拟合的广义单指标模型具有可识别性,我们首先采用了“消去一个分量”的方法对指标向量重参数化。然后,我们提出了基于广义估计方程的核估计方法和截面方法对广义单指标模型中的未知连接函数和指标向量的方向进行估计。我们证明了指标向量的(?)相合性,并且给出了广义单指标函数的渐进性质。另外,我们提出了拟费歇尔得分算法对连接函数和指标向量的方向进行迭代估计。
在本文的第五章,我们提出了一种基于分层似然的双惩罚方法,实现了对广义线性混合效应模型的固定效应和随机效应同时进行选择的目的。该方法不仅避免了高维积分来得到用于效应选择的目标函数,而且通过Cholesky分解保证了所选随机效应对应的协方差矩阵的正定性。我们证明了该方法在不需要损失函数的凸型条件下具有Oracle性质。而且,我们提出了一种两阶段算法来有效地实现这个方法,并提出了基于分层似然的贝叶斯信息准则用于对调整参数进行自动赋值。
通过大量的模拟实验我们比较了本文中提出的各方法和一些已有的方法,因而验证了这些新方法的有效性。另外,我们还将这些方法用于分析各种实际数据,比如交叉试验数据,抗癌抑制剂CCI-779的二期临床试验数据,癫痫发作次数数据以及多中心爱滋病群组研究的数据,说明了这些方法的应用价值所在。
This dissertation is devoted to methodology development for marginal models and mixed effects models in the literature of high-dimensional longitudinal data analysis.
Longitudinal data typically refers to the data containing cross-sectional and time series observations at different time points for a number of individuals. It arises frequently from psychological studies, social sciences, medical studies and biological sciences. Its major character is to put cross-sectional data and time series data together, so that it is able to not only analyse the trend of individuals, but also analyse the total change trend. Recently, many statisticians pay attention to various models of longitudinal data. And in this dissertation, we focus on two types of models:marginal models and mixed effects models. We discuss parameter estimation and variable selection under these two types of models in the high-dimensional longitudinal data analysis.
In Chapter2, for the logistic regression model, which is a special generalized linear model, we propose a two-stage shrinkage approach for simultaneous variable selection and parameter estimation. Its main idea is first to construct a weighted least-squares type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations model, and then to produce sparse estimation of the regression coefficients in the sprit of the adaptive Least Absolute Shrinkage and Selection Operator (Zou,2006). The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters, i.e., with probability tending to1, we select the subset consisting of all the indices of nonzero coefficients and the estimators of the nonzero coefficients have the asymptotic normality property. Moreover, we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified and develop a consistent penalized quadratic form function criterion for the selection of tuning parameter. Finally, we extend the technique to the general marginal longitudinal generalized linear models.
With rapid development of computing power and other modern technology, high-throughput data sets of unprecedented size and complexity are often encountered in many statistical studies, such as gene expression data from DNA microarray experiments. How-ever, there are virtually no solutions for feature screening in the ultra-high dimensional longitudinal gene expression data setting. To fill in this gap. we propose a novel GEE- based screening procedure in Chapter3, which only pertains to the specifications of the first two marginal moments and a working correlation strueture. Different from exist-ing screening methods, the new method merely involves making a single evaluation of estimating functions instead of fitting all separate marginal models or computing each pairwise correlation. And we show that the proposed method is robust with respect to the mis-specification of correlation structures and enjoys the sure screening property.
Motivated by an analysis of a real longitudinal data set from an epileptic seizure study, we suggest a marginal generalized single-index model in Chapter4. To well i-dentify the index in estimation, we first use the "remove-one-component" method for re-parametrization. Then, we suggest using a kernel GEE-type method to estimate the unknown link function and using a profile-type method to estimate the unknown index. We prove the estimator of the index is root-n consistent, and establish the asymptotic property of the nonparametric estimator of the generalized single-index function. A quasi-Fisher scoring type algorithm is also developed to estimate the unknown link function and the index iteratively.
In Chapter5, we develop a double penalized hierarchical likelihood for selecting fixed and random effects in generalized linear mixed models simultaneously. The proposed method not only avoids the calculation of high-dimensional integral to define an objective function for effect selection, but also guarantee the positive defmiteness of the covariance matrix of selected random effects through Cholesky decomposition. We show that the resulting estimator enjoys the oracle properties with no requirement on the convexity of loss function. Moreover, a two-stage algorithm is proposed to effectively implement this approach. And an H-likelihood-based Bayesian information criterion is developed for tuning parameter selection.
Moreover, we compare each proposal in this dissertation with its related alternatives by comprehensive simulation studies to illustrate the efficieney of our proposals. We also demonstrate the use of our proposals through a wide range of applications in real data analysis, such as the data from a crossover trial, a phase Ⅱ study of the anti-cancer inhibitor CCI-779, an epileptic seizure study, and a multi-center AIDS cohort study.
纵向数据是指对同一个个体或者试验单位在不同时间进行观测而得到的由截面和时间序列相融合的数据。它在心理学、社会学、医学以及生物学等科学领域中经常出现,其最大的特点是其将截面数据和时间序列数据结合在一起,既能分析出观测单元随时间变化的趋势,又能分析出总体的变化趋势。近年来,对纵向数据各种模型的研究引起了国内外统计学家的广泛关注。在本文中,我们主要研究了两类模型：边际模型和混合效应模型,探讨了它们在高维情况下的参数估计和变量选择的问题。
在本文的第二章,对于特殊的广义线性模型Logistic回归模型,我们提出了一种两阶段的收缩估计方法来同时进行变量选择和参数估计,其主要思路是在广义估计方程的非保守向量场内,通过引入一种特殊的加权机制来构造加权最小二乘型的函数,然后利用Zou[104]所提出的自适应性最小绝对缩减和变量选择算子得到回归系数的稀疏估计。我们在维数发散情况下,证明了该收缩估计方法具有Oracle性质,即模型选择过程的相合性和非零参数估计的渐进正态性。同时,我们对参数估计的协方差函数提出了一种相合的三明治估计,并且提出了相合的惩罚二次型准则来应对调整参数的选取。最后,我们讨论了一般广义线性模型下该收缩方法的应用。
随着计算机计算技术和其他现代技术的发展,使得收集和处理海量复杂数据己成为可能,比如利用DNA微阵列技术收集到的基因表达数据。但是,在纵向数据情况下,超高维基因数据的特征选择一直没有得到很好的解决,因此,为了填补这一空白,在本文第三章中我们提出了一种基于广义估计方程的筛选准则,它只须对一二阶矩和工作相关系数矩阵进行假定。不同于文献中已有的筛选方法,该方法无须拟合所有的边际模型或计算配对相关性,它只须通过对估计函数计算一次即可快速完成特征的选择。同时我们还证明了该方法具有稳健性,即使在工作相关系数矩阵错误假定下,仍然具有Sure Screening性质。
本文的第四章是通过对关于癫痫发作次数的某实际数据的观察,提出了广义单指标模型来对数据建模。为了让拟合的广义单指标模型具有可识别性,我们首先采用了“消去一个分量”的方法对指标向量重参数化。然后,我们提出了基于广义估计方程的核估计方法和截面方法对广义单指标模型中的未知连接函数和指标向量的方向进行估计。我们证明了指标向量的(?)相合性,并且给出了广义单指标函数的渐进性质。另外,我们提出了拟费歇尔得分算法对连接函数和指标向量的方向进行迭代估计。
在本文的第五章,我们提出了一种基于分层似然的双惩罚方法,实现了对广义线性混合效应模型的固定效应和随机效应同时进行选择的目的。该方法不仅避免了高维积分来得到用于效应选择的目标函数,而且通过Cholesky分解保证了所选随机效应对应的协方差矩阵的正定性。我们证明了该方法在不需要损失函数的凸型条件下具有Oracle性质。而且,我们提出了一种两阶段算法来有效地实现这个方法,并提出了基于分层似然的贝叶斯信息准则用于对调整参数进行自动赋值。
通过大量的模拟实验我们比较了本文中提出的各方法和一些已有的方法,因而验证了这些新方法的有效性。另外,我们还将这些方法用于分析各种实际数据,比如交叉试验数据,抗癌抑制剂CCI-779的二期临床试验数据,癫痫发作次数数据以及多中心爱滋病群组研究的数据,说明了这些方法的应用价值所在。
This dissertation is devoted to methodology development for marginal models and mixed effects models in the literature of high-dimensional longitudinal data analysis.
Longitudinal data typically refers to the data containing cross-sectional and time series observations at different time points for a number of individuals. It arises frequently from psychological studies, social sciences, medical studies and biological sciences. Its major character is to put cross-sectional data and time series data together, so that it is able to not only analyse the trend of individuals, but also analyse the total change trend. Recently, many statisticians pay attention to various models of longitudinal data. And in this dissertation, we focus on two types of models:marginal models and mixed effects models. We discuss parameter estimation and variable selection under these two types of models in the high-dimensional longitudinal data analysis.
In Chapter2, for the logistic regression model, which is a special generalized linear model, we propose a two-stage shrinkage approach for simultaneous variable selection and parameter estimation. Its main idea is first to construct a weighted least-squares type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations model, and then to produce sparse estimation of the regression coefficients in the sprit of the adaptive Least Absolute Shrinkage and Selection Operator (Zou,2006). The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters, i.e., with probability tending to1, we select the subset consisting of all the indices of nonzero coefficients and the estimators of the nonzero coefficients have the asymptotic normality property. Moreover, we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified and develop a consistent penalized quadratic form function criterion for the selection of tuning parameter. Finally, we extend the technique to the general marginal longitudinal generalized linear models.
With rapid development of computing power and other modern technology, high-throughput data sets of unprecedented size and complexity are often encountered in many statistical studies, such as gene expression data from DNA microarray experiments. How-ever, there are virtually no solutions for feature screening in the ultra-high dimensional longitudinal gene expression data setting. To fill in this gap. we propose a novel GEE- based screening procedure in Chapter3, which only pertains to the specifications of the first two marginal moments and a working correlation strueture. Different from exist-ing screening methods, the new method merely involves making a single evaluation of estimating functions instead of fitting all separate marginal models or computing each pairwise correlation. And we show that the proposed method is robust with respect to the mis-specification of correlation structures and enjoys the sure screening property.
Motivated by an analysis of a real longitudinal data set from an epileptic seizure study, we suggest a marginal generalized single-index model in Chapter4. To well i-dentify the index in estimation, we first use the "remove-one-component" method for re-parametrization. Then, we suggest using a kernel GEE-type method to estimate the unknown link function and using a profile-type method to estimate the unknown index. We prove the estimator of the index is root-n consistent, and establish the asymptotic property of the nonparametric estimator of the generalized single-index function. A quasi-Fisher scoring type algorithm is also developed to estimate the unknown link function and the index iteratively.
In Chapter5, we develop a double penalized hierarchical likelihood for selecting fixed and random effects in generalized linear mixed models simultaneously. The proposed method not only avoids the calculation of high-dimensional integral to define an objective function for effect selection, but also guarantee the positive defmiteness of the covariance matrix of selected random effects through Cholesky decomposition. We show that the resulting estimator enjoys the oracle properties with no requirement on the convexity of loss function. Moreover, a two-stage algorithm is proposed to effectively implement this approach. And an H-likelihood-based Bayesian information criterion is developed for tuning parameter selection.
Moreover, we compare each proposal in this dissertation with its related alternatives by comprehensive simulation studies to illustrate the efficieney of our proposals. We also demonstrate the use of our proposals through a wide range of applications in real data analysis, such as the data from a crossover trial, a phase Ⅱ study of the anti-cancer inhibitor CCI-779, an epileptic seizure study, and a multi-center AIDS cohort study.
引文
[1]Ahn, M., Zhang. H.H. and Lu, W.B. (2011). Moment-based method for random effects selection in linear mixed models. To appear in Statistica Sinica.
[2]Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory(Ed. B.N. Petrov and F. Csaki), pp.267-281. BudapestL Akademiai Kiado.
[3]Bai, Y., Fung, W.K., and Zhu, Z.Y. (2009). Penalized quadratic inference functions for single-index models with longitudinal data. Journal of Multivariate Analysis 100,152-161.
[4]Balan, R.M. and Schiopu-Kratina, Ⅰ. (2005). Asymptotic results with generalized estimating equations for longitudinal data. The Annals of Statistics 32,522-541.
[5]Bolker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, M.H., and While, J.S. (2009). Generalized linear mixed models:a practical guide for ecology and evolu-tion. Trends in Ecology and Evolution 24,127-135.
[6]Bondell, H.D., Krishna, A., and Ghosh, S.K. (2010). Joint variable selection for fixed and random effects in linear mixed-effects models. Biometrics 66,1069-1077.
[7]Boni, J.P., Leister, C., Bender, G., Fitzpatrick, P.V., Twine, N., Stover, J., Dorner, A. Immermann, F., and Burczynski, M. (2005). Population pharmacokinetics of CCI-779:Cor-relations to safety and pharmacogenomic responses in patients with advanced renal cancer. Clinical Pharmacology and Therapeutics 77,76-89.
[8]Breslow, N.E. and Clayton, D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88,9-25.
[9]Cantoni, E., Flemming, J.M. and Ronchetti, E. (2005). Variable selection for marginal lon-gitudinal generalized linear models. Biometrics 61,507-514.
[10]Cantoni, E., Filed, C., Flemming, J.M. and Ronchetti, E. (2005). Longitudinal variable selection by cross-validation in the case of many covariates. Statistics in Medicine 26,919-930.
[11]Carroll, R.J., Fan, J.Q., Gijbels, I., and Wand, M.P. (1997). Generalized partially linear single-index models. Journal of the American Statistical Association 92,477-489.
[12]Chen.Z. and Dunson.D.B. (2003). Random effects selection in linear mixed models. Bio-metrics 59,762-769.
[13]Cui, X., Haddle, W.K., and Zhu, L.X. (2011). The EFM approach for single-index models. The Annals of Statistics 39,1658-1688.
[14]Diggle, P.J., Heagerty, P.J., Liang, K.Y. and Zeger, S.L. (2002). Analysis of Longitudinal Data.2nd edition, Oxford University Press.
[15]Dziak, J.J. (2006). Penalized quadratic inference functions for variable selec-tion in longitudinal research, Ph.D. Thesis, the Pennsylvania State University. (http://www.stat.psu.edu/jdziak)
[16]Dziak, J.J. and Li. R.Z. (2006). An overview on variable selection for longitudinal data. In D. Hong, editor, Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques. Chapter One. World Scientific Publishing Co. Pte. Ltd., Singapore,2006.
[17]Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004). Least Angle Regression. The Annals of Statistics 32,407-499.
[18]Fan, J.Q., Feng, Y., and Song, R. (2011). Nonparametric independence screening in sparse ultra-high dimensional additive models. Journal of the American Statistical Association 116, 544-557.
[19]Fan, J.Q., Gijbels, I., Hu, T.C., and Huang, L.S. (1995). A study of variable bandwidth selection for local polynomial regression. Statistica Sinica 6,113-127.
[20]Fan, J.Q. and Li, R.Z. (2001). Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties. Journal of the American Statistical Association 96,1348-1359.
[21]Fan, J.Q. and Li, R.Z. (2004). New estimation and model selection procedures for semipara-metric modeling in longitudinal data analysis. Journal of the American Statistical Association 99,710-723.
[22]Fan, J.Q. and Lv, J.C. (2008). Sure independence screening for ultrahigh dimensional fea-ture space (with discussion). Journal of the Royal Statistical Society, Series B 70,849-911.
[23]Fan, J.Q., Samworth, R., and Wu, Y.C. (2009). Ultrahigh dimension variable selection: beyond the linear model. Journal of Machine Learning Research 10,1829-1853.
[24]Fan, J.Q. and Song, R. (2010). Sure Independence Screening in Generalized Linear Models with NP-dimensionality. The Annals of Statistics 38,3567-3604.
[25]Foster, S.D., Verbyla, A.P., and Pitchford, W.S. (2009). Estimation, prediction and infer-ence for the LASSO random effect models. Australian and New Zealand Journal of Statistics 51,43-61.
[26]Fu, W.J. (2003). Penalized estimating equations. Biometrics 59,126-132.
[27]Hall, D.B. and Severini, T.A. (1998). Extended Generalized Estimating Equations for Clus-tered Data. Journal of the American Statistical Association 93,1365-1375.
[28]Hardle, W.K., Hall, P., and Ichimura, H. (1993). Optimal smoothing in single-index models. The Annals of Statistics 21,157-178.
[29]Hristache, M.. Juditski. A., and Spokoiny. V. (2001). Direct estimation of the index coeffi-cients in a single-index model. The Annals of Statistics 29,595-623.
[30]Huang, J.Z.,Wu. CO., and Zhou, L. (2002). Varying-Coefficient Models and Basis Function Approximations for the Analysis of Repeated Measurements. Biometrika 89,111-128.
[31]Ichimura, H. (1993). Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. Journal of Econometrics 58,71-120.
[32]Ibrahim, J.G., Zhu, H.T., Garcia. R.I.,and Guo, R.X. (2011). Fixed and random effects selection in mixed effects models. Biometrics 67,495-503.
[33]Jiang, C.R. and Wang, J.L. (2011). Functional single index models for longitudinal data. The Annals of Statistics 39,362-388.
[34]Jiang, J.M. (1999). Conditional inference about generalized linear mixed models. The An-nals of Statistics 27,1974-2007.
[35]Jiang, J.M. (2007). Linear and Generalized Linear Mixed Models and Their Applications. Springer, New York.
[36]Jiang, J.M., Jia, H., and Chen, H. (2001). Maximum posterior estimation of random effects in generalized linear mixed models. Statistica Sinica 11,97-120.
[37]Jiang, J.M., Rao, J.S., Gu, Z.H., and Nguye T. (2008). Fence methods for mixed model selection. The Annals of Statistics 36,1669-1692.
[38]Jones, B. and Kenward, M.G. (1987). Modelling binary data from a three-point cross-over trail. Statistics in Medicine 6,555-564.
[39]Kaslow, R.A., Ostrow, D.G., Detels, R., Phair, J.P., Polk, B.F., and Rinaldo, C.R. (1987). The Multicenter AIDS Cohort Study:Rationale, organization and selected characteristics of the participants. American Journal Epidemiology 126,310-318.
[40]Lan, L. (2006). Variable selection in linear mixed model for longitudinal data. Ph.D. Thesis, North Carolina State University.
[41]Lange, N. and Laird. N.M. (1989). The effect of covariance structures on variance estimation in balance growth-curve models with random parameters. Journal of the American Statistical Association 84,241-247.
[42]Lee, Y. and Nelder, J.A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society, Series B 58,619-678.
[43]Lee, Y., Nelder, J.A., and Pawitan, Y. (2006). Generalized Linear Models with Random Effects:Unified Analysis via H-likelihood. Chapman and Hall. London.
[44]Leng, C.L. and Li, B. (2010). Least squares approximation with a diverging number of parameters. Statistics and Probability Letters 80,254-261.
[45]Leung, H.Y., Wang, Y.G., and Zhu, M. (2009). Efficient parameter esimation in longitudinal data analysisi using a hybrid GEE method. Biostatistics 10,436-445.
[46]Li, R.Z., Zhong, W., and Zhu, L.P. (2012). Feature screening via distance correlation learn-ing. To appear in Journal of the American Statistical Association.
[47]Li, Y., Wang, S.J., Song, Peter X.K., Wang, N., and Zhu, J. (2011). Doubly regularized estimation and selection in linear mixed-effects models for high-dimensinal longitudinal data. Manuscript.
[48]Li, Y.H., Wang, N., and Carroll, R.J. (2010). Generalized functional linear models with semiparametric single-index interactions. Journal of the American Statistical Association 105, 621-633.
[49]Liang, H., Wu, H.L., and Zou, G.H. (2008). A note on conditional AIC for linear mixed-effects models. Biometrika 95,773-778.
[50]Liang, K.Y. and Zeger, S.L. (1986). Longitudinal data analysis using generalised linear models. Biometrika 73,12-22.
[51]Mack, Y.P. and Silverman, B.W. (1982). Weak and strong uniform consistency of kernel regression estimates. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 405-415.
[52]McGilchrist, C.A. (1994). Estimation in generalized mixed models. Journal of the Royal Statistical Society, Series B 56,61-69.
[53]Meng, X.L. (2009). Decoding the H-likelihood. Statistical Science 24,280-293.
[54]Miyake, H., Gleave, M., Arakawa, S., Kamidono, S., and Hara, Ⅰ. (2002). Introducing the clusterin gene into human renal cell carcinoma cells enhances their metastatic potential. The Journal of Urology 167,2203-2208.
[55]Ni, X., Zhang, D.W., and Zhang, H.H. (2010). Variable selection for semiparametric mixed models in longitudinal studies. Biometrics 66,79-88.
[56]Niers, T.M.H., Richel, D.J., Meijers, J.C.M., and Schlingemann, R.O. (2011). Vascular endothelial growth factor in the circulation in cancer patients may not be a relevant biomarker. PLoS ONE 6, e19873.
[57]Oman, S.D. (2009). Easily simulated multivariate binary distributions with given positive and negative correlations. Computational Statistics and Data Analysis 53,999-1005.
[58]Pan, W. (2001). Akaike's Information Criterion in generalized estimating equations. Bio-metrics 57,120-125.
[59]Peng, H. and Lu, Y. (2012). Models selection in linear mixed effect models. Journal of Multivariate Analysis 109,109-129.
Pepe, M.S. and Anderson. G.L. (1994). A cautionary note on inference for marginal regres-sion models with longitudinal data and general correlated response data. Communications in Statistics, Simulation and Compution 23.939-951.
[61]Powell, J.L., Stock, J.H., and Stoker, T.M. (1989). Semiparametric estimation of index coefficients. Econometrica 57,1403-1430.
[62]Prentice, R.L. and Zhao, L.P. (1991). Estimating Equations for Parameters in Means and Covariances of Multivariate Discrete and Continuous Responses. Biometrics 47,825-839.
[63]Pu. W.J. and Niu, X.F. (2006). Selecting mixed-effects models based on a generalized information criterion. Journal of Multivariate Analysis 97,733-758.
[64]Qu, A., Lindsay, B.G., and Li, B. (2000). Improving Generalised Estimating Equations Using Quadratic Inference Functions. Biometrika 87,823-836.
[65]Rao, C.R. and Wu, Y. (1989). A strongly consistent procedure for model selection in a regression problem. Biometrika 76,369-374.
[66]Romaschin, A.D., Youssef, Y., Chow, T.F., Siu, K.W., DeSouza, L.V., Honey, R.J., Stewart, R., Pace, K.T., and Yousef, G.M. (2009). Exploring the pathogenesis of renal cell carcinoma: pathway and bioinformatics analysis of dysregulated genes and proteins. Biological Chemistry 390,125-135.
[67]Schelldorfer, J., Buhlmann, P. and van de Geer, S. (2011). Estimation for high-dimensional linear mixed-effects models using l1-penalization. Scandinavian Journal of Statistics 38,197-214.
[68]Schelldorfer, J. and Buhlmann, P. (2011). GLMMLasso:An algorithm for high-dimensional generalized linear mixed models using l1-penalization. In press.
[69]Schlegel, P.N., Matthews, G.J., Cichon. Z., Aulitzky, W.K., Cheng, C.Y., Chen, C.L. Saso, L., Goldstein, M., Jdnne, O.A., and Bardin. C.W. (1992). Clusterin production in the obstructed rabbit kidney:correlations with loss of renal function. Journal of the American Society of Nephrology 3,1163-1171.
[70]Schmid, H., Cohen, CD., Henger, A., Irrgang, S., Schlondorff. D., and Kretzler, M. (2003). Validation of endogenous controls for gene expression analysis in microdissected human renal biopsies. Kidney International 64,356-360.
[71]Schwartz, G. (1978). Estimating the dimensions of a model. The Annals of Statistics 6, 461-464.
[72]Song Peter X.K. (2007). Correlated Data Analysis:Modeling, Analytics, and Applications. Springer, New York.
[73]Thall, P. and Vail. S.C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics 46,657-671.
[74]Tierney, L. and Kadane, J.B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association 81,82-86.
[75]Vaida, F. and Blanchard,S. (2005). Conditional Akaike information for mixed-effects mod-els. Biometrika 92,351-370.
[76]van der Vaart, A.W. and Wellner, J.A. (1996). Weak Convergence and Empirical Processes. Springer-Verlag New York Inc.
[77]Verbeke, G. and Molenberghs G. (2000). Linear Mixed Models for Longitudinal Data. Springer-Verlag New York Inc.
[78]Vonesh, E., Wang, H., Nie, L., and Majumdar, D. (2002). Conditional second-order gener-alized estimating equations for generalized linear and nonlinear mixed-effects models. Journal of the American Statistical Association 97,271-283.
[79]Wang, H. and Leng, C. (2007). Unified lasso estimation via least square approximation. Journal of the American Statistical Association 102,1039-1048.
[80]Wang, H., Li, R. and Tsai, C.L. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika 94,553-568.
[81]Wang, J.L., Xue, L.G., Zhu, L.X., and Chong, Y.S. (2010). Partial-linear single-index model with noised variable. The Annals of Statistics 38,246-272.
[82]Wang, L. (2011). GEE analysis of clustered binary data with diverging number of covariates. The Annals of Statistics 39,389-417.
[83]Wang, L. and Qu, A. (2009). Consistent model selection and data-driven smooth tests for longitudinal data in the estimating equations approach. Journal of the Royal Statistical Society, Series B 71,177-190.
[84]Wang, L., Zhou, J.H., and Qu, A. (2011). High-dimensional penalized generalized estimat-ing equations for longitudinal data analysis. To appear in Biometrics.
[85]Wang, N. (2003). Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika 90,43-52.
[86]Wang. N.,Carroll, R.J.,and Lin. X.H. (2005). Efficient semiparametric marginal estimation for longitudinal/clustered data. Journal of the American Statistical Association 100,147-157.
[87]Wang, S.J., Song, Peter X.K., and Zhu, J. (2010). Doubly regularized REML for esti-mation and selection of fixed and random effects in linear mixed-effects models. The Uni-versity of Michigan Department of Biostatistics Working Paper Series. Working Paper 89. http://biostats.bepress.com/umichbiostat/paper89
[88]Wang, Y.G., Lin, X.H., and Zhu, M. (2005). Robust estimating functions and bias correction for longitudinal data analysis. Biometrics 61,684-691.
White, H. (1994). Estimation, Inference, and Specification Analysis. Cambridge University Press, New York.
[90]Xia, Y.C., Tong, H., Li, W.K., and Zhu, L.X. (2002). An adaptive estimation of dimension reduction space. Journal of the Royal Statistical Society, Series B 64,363-410.
[91]Xie, M.G. and Yang, Y.N. (2003). Asymptotics for generalized estimating equations with large cluster sizes. The Annals of Statistics 31,310-347.
[92]Xu, P.R., Fu, W.J., and Zhu, L.X. (2013). Shrinkage estimation analysis of correlated binary data with a diverging number of parameters. Science China Mathematic 56,359-377.
[93]Yahav, I. and Shmueli, G. (2009). On Generating Multivariate Poisson Data in Management Science Applications. Applied Stochastic Models in Business and Industry 28,91-102.
[94]Yang, H.M. (2007). Variable selection procedures for generazlied linear mixed models in longitudinal data analysis, Ph.D. Thesis, North Carolina State University.
[95]Yi, G.Y., He, W.Q., and Liang, H. (2009). Analysis of correlated binary data under partially linear single-index logistic models. Journal of Multivariate Analysis 100,278-290.
[96]Yi, G.Y., He, W.Q., and Liang, H. (2011). Semiparametric marginal and association re-gression methods for clustered binary data. Annals of Institute of Statistical Mathematics 63, 511-533.
[97]Yu. Y. and Ruppert, D. (2002). Penalized Spline Estimation for Partially Linear Single-Index Models. Journal of the American Statistical Association 97,1042-1054.
[98]Zhang, C.H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics 38,894-942.
[99]Zhao, S.D. and Li, Y. (2012). Principled sure independence screening for Cox models with ultra-high-dimensional covariates. Journal of Multivariate Analysis 105,397-411.
[100]Zhao, S.D. and Li, Y. (2012). Sure screening for estimating equations in ultra-high dimen-sions. http://arxiv.org/pdf/1110.6817.pdf.
[101]Zhu. L.P.. Li. L.X., Li. R.Z., and Zhu, L.X. (2011). Model-free feature screening for ultrahigh-dimensional data. Journal of the American Statistical Association 106.1464-1475.
[102]Zhu. L.X. and Xue. L.G. (2006). Empirical likelihood confidence regions in a partially linear single-index model. Journal of the Royal Statistical Society, Series B 68,549-570.
[103]Zipunnikov. V.V. and Booth, J.G. (2006). Monte Carlo EM for Generalized Linear Mixed Models using Randomized Spherical Radial Integration, manuscript.
[104]Zou. H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association 101.1418-1429.
[105]Zou, H. and Zhang, H.H. (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics 37,1733-1751.
[2]Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory(Ed. B.N. Petrov and F. Csaki), pp.267-281. BudapestL Akademiai Kiado.
[3]Bai, Y., Fung, W.K., and Zhu, Z.Y. (2009). Penalized quadratic inference functions for single-index models with longitudinal data. Journal of Multivariate Analysis 100,152-161.
[4]Balan, R.M. and Schiopu-Kratina, Ⅰ. (2005). Asymptotic results with generalized estimating equations for longitudinal data. The Annals of Statistics 32,522-541.
[5]Bolker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, M.H., and While, J.S. (2009). Generalized linear mixed models:a practical guide for ecology and evolu-tion. Trends in Ecology and Evolution 24,127-135.
[6]Bondell, H.D., Krishna, A., and Ghosh, S.K. (2010). Joint variable selection for fixed and random effects in linear mixed-effects models. Biometrics 66,1069-1077.
[7]Boni, J.P., Leister, C., Bender, G., Fitzpatrick, P.V., Twine, N., Stover, J., Dorner, A. Immermann, F., and Burczynski, M. (2005). Population pharmacokinetics of CCI-779:Cor-relations to safety and pharmacogenomic responses in patients with advanced renal cancer. Clinical Pharmacology and Therapeutics 77,76-89.
[8]Breslow, N.E. and Clayton, D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88,9-25.
[9]Cantoni, E., Flemming, J.M. and Ronchetti, E. (2005). Variable selection for marginal lon-gitudinal generalized linear models. Biometrics 61,507-514.
[10]Cantoni, E., Filed, C., Flemming, J.M. and Ronchetti, E. (2005). Longitudinal variable selection by cross-validation in the case of many covariates. Statistics in Medicine 26,919-930.
[11]Carroll, R.J., Fan, J.Q., Gijbels, I., and Wand, M.P. (1997). Generalized partially linear single-index models. Journal of the American Statistical Association 92,477-489.
[12]Chen.Z. and Dunson.D.B. (2003). Random effects selection in linear mixed models. Bio-metrics 59,762-769.
[13]Cui, X., Haddle, W.K., and Zhu, L.X. (2011). The EFM approach for single-index models. The Annals of Statistics 39,1658-1688.
[14]Diggle, P.J., Heagerty, P.J., Liang, K.Y. and Zeger, S.L. (2002). Analysis of Longitudinal Data.2nd edition, Oxford University Press.
[15]Dziak, J.J. (2006). Penalized quadratic inference functions for variable selec-tion in longitudinal research, Ph.D. Thesis, the Pennsylvania State University. (http://www.stat.psu.edu/jdziak)
[16]Dziak, J.J. and Li. R.Z. (2006). An overview on variable selection for longitudinal data. In D. Hong, editor, Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques. Chapter One. World Scientific Publishing Co. Pte. Ltd., Singapore,2006.
[17]Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004). Least Angle Regression. The Annals of Statistics 32,407-499.
[18]Fan, J.Q., Feng, Y., and Song, R. (2011). Nonparametric independence screening in sparse ultra-high dimensional additive models. Journal of the American Statistical Association 116, 544-557.
[19]Fan, J.Q., Gijbels, I., Hu, T.C., and Huang, L.S. (1995). A study of variable bandwidth selection for local polynomial regression. Statistica Sinica 6,113-127.
[20]Fan, J.Q. and Li, R.Z. (2001). Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties. Journal of the American Statistical Association 96,1348-1359.
[21]Fan, J.Q. and Li, R.Z. (2004). New estimation and model selection procedures for semipara-metric modeling in longitudinal data analysis. Journal of the American Statistical Association 99,710-723.
[22]Fan, J.Q. and Lv, J.C. (2008). Sure independence screening for ultrahigh dimensional fea-ture space (with discussion). Journal of the Royal Statistical Society, Series B 70,849-911.
[23]Fan, J.Q., Samworth, R., and Wu, Y.C. (2009). Ultrahigh dimension variable selection: beyond the linear model. Journal of Machine Learning Research 10,1829-1853.
[24]Fan, J.Q. and Song, R. (2010). Sure Independence Screening in Generalized Linear Models with NP-dimensionality. The Annals of Statistics 38,3567-3604.
[25]Foster, S.D., Verbyla, A.P., and Pitchford, W.S. (2009). Estimation, prediction and infer-ence for the LASSO random effect models. Australian and New Zealand Journal of Statistics 51,43-61.
[26]Fu, W.J. (2003). Penalized estimating equations. Biometrics 59,126-132.
[27]Hall, D.B. and Severini, T.A. (1998). Extended Generalized Estimating Equations for Clus-tered Data. Journal of the American Statistical Association 93,1365-1375.
[28]Hardle, W.K., Hall, P., and Ichimura, H. (1993). Optimal smoothing in single-index models. The Annals of Statistics 21,157-178.
[29]Hristache, M.. Juditski. A., and Spokoiny. V. (2001). Direct estimation of the index coeffi-cients in a single-index model. The Annals of Statistics 29,595-623.
[30]Huang, J.Z.,Wu. CO., and Zhou, L. (2002). Varying-Coefficient Models and Basis Function Approximations for the Analysis of Repeated Measurements. Biometrika 89,111-128.
[31]Ichimura, H. (1993). Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. Journal of Econometrics 58,71-120.
[32]Ibrahim, J.G., Zhu, H.T., Garcia. R.I.,and Guo, R.X. (2011). Fixed and random effects selection in mixed effects models. Biometrics 67,495-503.
[33]Jiang, C.R. and Wang, J.L. (2011). Functional single index models for longitudinal data. The Annals of Statistics 39,362-388.
[34]Jiang, J.M. (1999). Conditional inference about generalized linear mixed models. The An-nals of Statistics 27,1974-2007.
[35]Jiang, J.M. (2007). Linear and Generalized Linear Mixed Models and Their Applications. Springer, New York.
[36]Jiang, J.M., Jia, H., and Chen, H. (2001). Maximum posterior estimation of random effects in generalized linear mixed models. Statistica Sinica 11,97-120.
[37]Jiang, J.M., Rao, J.S., Gu, Z.H., and Nguye T. (2008). Fence methods for mixed model selection. The Annals of Statistics 36,1669-1692.
[38]Jones, B. and Kenward, M.G. (1987). Modelling binary data from a three-point cross-over trail. Statistics in Medicine 6,555-564.
[39]Kaslow, R.A., Ostrow, D.G., Detels, R., Phair, J.P., Polk, B.F., and Rinaldo, C.R. (1987). The Multicenter AIDS Cohort Study:Rationale, organization and selected characteristics of the participants. American Journal Epidemiology 126,310-318.
[40]Lan, L. (2006). Variable selection in linear mixed model for longitudinal data. Ph.D. Thesis, North Carolina State University.
[41]Lange, N. and Laird. N.M. (1989). The effect of covariance structures on variance estimation in balance growth-curve models with random parameters. Journal of the American Statistical Association 84,241-247.
[42]Lee, Y. and Nelder, J.A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society, Series B 58,619-678.
[43]Lee, Y., Nelder, J.A., and Pawitan, Y. (2006). Generalized Linear Models with Random Effects:Unified Analysis via H-likelihood. Chapman and Hall. London.
[44]Leng, C.L. and Li, B. (2010). Least squares approximation with a diverging number of parameters. Statistics and Probability Letters 80,254-261.
[45]Leung, H.Y., Wang, Y.G., and Zhu, M. (2009). Efficient parameter esimation in longitudinal data analysisi using a hybrid GEE method. Biostatistics 10,436-445.
[46]Li, R.Z., Zhong, W., and Zhu, L.P. (2012). Feature screening via distance correlation learn-ing. To appear in Journal of the American Statistical Association.
[47]Li, Y., Wang, S.J., Song, Peter X.K., Wang, N., and Zhu, J. (2011). Doubly regularized estimation and selection in linear mixed-effects models for high-dimensinal longitudinal data. Manuscript.
[48]Li, Y.H., Wang, N., and Carroll, R.J. (2010). Generalized functional linear models with semiparametric single-index interactions. Journal of the American Statistical Association 105, 621-633.
[49]Liang, H., Wu, H.L., and Zou, G.H. (2008). A note on conditional AIC for linear mixed-effects models. Biometrika 95,773-778.
[50]Liang, K.Y. and Zeger, S.L. (1986). Longitudinal data analysis using generalised linear models. Biometrika 73,12-22.
[51]Mack, Y.P. and Silverman, B.W. (1982). Weak and strong uniform consistency of kernel regression estimates. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 405-415.
[52]McGilchrist, C.A. (1994). Estimation in generalized mixed models. Journal of the Royal Statistical Society, Series B 56,61-69.
[53]Meng, X.L. (2009). Decoding the H-likelihood. Statistical Science 24,280-293.
[54]Miyake, H., Gleave, M., Arakawa, S., Kamidono, S., and Hara, Ⅰ. (2002). Introducing the clusterin gene into human renal cell carcinoma cells enhances their metastatic potential. The Journal of Urology 167,2203-2208.
[55]Ni, X., Zhang, D.W., and Zhang, H.H. (2010). Variable selection for semiparametric mixed models in longitudinal studies. Biometrics 66,79-88.
[56]Niers, T.M.H., Richel, D.J., Meijers, J.C.M., and Schlingemann, R.O. (2011). Vascular endothelial growth factor in the circulation in cancer patients may not be a relevant biomarker. PLoS ONE 6, e19873.
[57]Oman, S.D. (2009). Easily simulated multivariate binary distributions with given positive and negative correlations. Computational Statistics and Data Analysis 53,999-1005.
[58]Pan, W. (2001). Akaike's Information Criterion in generalized estimating equations. Bio-metrics 57,120-125.
[59]Peng, H. and Lu, Y. (2012). Models selection in linear mixed effect models. Journal of Multivariate Analysis 109,109-129.
Pepe, M.S. and Anderson. G.L. (1994). A cautionary note on inference for marginal regres-sion models with longitudinal data and general correlated response data. Communications in Statistics, Simulation and Compution 23.939-951.
[61]Powell, J.L., Stock, J.H., and Stoker, T.M. (1989). Semiparametric estimation of index coefficients. Econometrica 57,1403-1430.
[62]Prentice, R.L. and Zhao, L.P. (1991). Estimating Equations for Parameters in Means and Covariances of Multivariate Discrete and Continuous Responses. Biometrics 47,825-839.
[63]Pu. W.J. and Niu, X.F. (2006). Selecting mixed-effects models based on a generalized information criterion. Journal of Multivariate Analysis 97,733-758.
[64]Qu, A., Lindsay, B.G., and Li, B. (2000). Improving Generalised Estimating Equations Using Quadratic Inference Functions. Biometrika 87,823-836.
[65]Rao, C.R. and Wu, Y. (1989). A strongly consistent procedure for model selection in a regression problem. Biometrika 76,369-374.
[66]Romaschin, A.D., Youssef, Y., Chow, T.F., Siu, K.W., DeSouza, L.V., Honey, R.J., Stewart, R., Pace, K.T., and Yousef, G.M. (2009). Exploring the pathogenesis of renal cell carcinoma: pathway and bioinformatics analysis of dysregulated genes and proteins. Biological Chemistry 390,125-135.
[67]Schelldorfer, J., Buhlmann, P. and van de Geer, S. (2011). Estimation for high-dimensional linear mixed-effects models using l1-penalization. Scandinavian Journal of Statistics 38,197-214.
[68]Schelldorfer, J. and Buhlmann, P. (2011). GLMMLasso:An algorithm for high-dimensional generalized linear mixed models using l1-penalization. In press.
[69]Schlegel, P.N., Matthews, G.J., Cichon. Z., Aulitzky, W.K., Cheng, C.Y., Chen, C.L. Saso, L., Goldstein, M., Jdnne, O.A., and Bardin. C.W. (1992). Clusterin production in the obstructed rabbit kidney:correlations with loss of renal function. Journal of the American Society of Nephrology 3,1163-1171.
[70]Schmid, H., Cohen, CD., Henger, A., Irrgang, S., Schlondorff. D., and Kretzler, M. (2003). Validation of endogenous controls for gene expression analysis in microdissected human renal biopsies. Kidney International 64,356-360.
[71]Schwartz, G. (1978). Estimating the dimensions of a model. The Annals of Statistics 6, 461-464.
[72]Song Peter X.K. (2007). Correlated Data Analysis:Modeling, Analytics, and Applications. Springer, New York.
[73]Thall, P. and Vail. S.C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics 46,657-671.
[74]Tierney, L. and Kadane, J.B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association 81,82-86.
[75]Vaida, F. and Blanchard,S. (2005). Conditional Akaike information for mixed-effects mod-els. Biometrika 92,351-370.
[76]van der Vaart, A.W. and Wellner, J.A. (1996). Weak Convergence and Empirical Processes. Springer-Verlag New York Inc.
[77]Verbeke, G. and Molenberghs G. (2000). Linear Mixed Models for Longitudinal Data. Springer-Verlag New York Inc.
[78]Vonesh, E., Wang, H., Nie, L., and Majumdar, D. (2002). Conditional second-order gener-alized estimating equations for generalized linear and nonlinear mixed-effects models. Journal of the American Statistical Association 97,271-283.
[79]Wang, H. and Leng, C. (2007). Unified lasso estimation via least square approximation. Journal of the American Statistical Association 102,1039-1048.
[80]Wang, H., Li, R. and Tsai, C.L. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika 94,553-568.
[81]Wang, J.L., Xue, L.G., Zhu, L.X., and Chong, Y.S. (2010). Partial-linear single-index model with noised variable. The Annals of Statistics 38,246-272.
[82]Wang, L. (2011). GEE analysis of clustered binary data with diverging number of covariates. The Annals of Statistics 39,389-417.
[83]Wang, L. and Qu, A. (2009). Consistent model selection and data-driven smooth tests for longitudinal data in the estimating equations approach. Journal of the Royal Statistical Society, Series B 71,177-190.
[84]Wang, L., Zhou, J.H., and Qu, A. (2011). High-dimensional penalized generalized estimat-ing equations for longitudinal data analysis. To appear in Biometrics.
[85]Wang, N. (2003). Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika 90,43-52.
[86]Wang. N.,Carroll, R.J.,and Lin. X.H. (2005). Efficient semiparametric marginal estimation for longitudinal/clustered data. Journal of the American Statistical Association 100,147-157.
[87]Wang, S.J., Song, Peter X.K., and Zhu, J. (2010). Doubly regularized REML for esti-mation and selection of fixed and random effects in linear mixed-effects models. The Uni-versity of Michigan Department of Biostatistics Working Paper Series. Working Paper 89. http://biostats.bepress.com/umichbiostat/paper89
[88]Wang, Y.G., Lin, X.H., and Zhu, M. (2005). Robust estimating functions and bias correction for longitudinal data analysis. Biometrics 61,684-691.
White, H. (1994). Estimation, Inference, and Specification Analysis. Cambridge University Press, New York.
[90]Xia, Y.C., Tong, H., Li, W.K., and Zhu, L.X. (2002). An adaptive estimation of dimension reduction space. Journal of the Royal Statistical Society, Series B 64,363-410.
[91]Xie, M.G. and Yang, Y.N. (2003). Asymptotics for generalized estimating equations with large cluster sizes. The Annals of Statistics 31,310-347.
[92]Xu, P.R., Fu, W.J., and Zhu, L.X. (2013). Shrinkage estimation analysis of correlated binary data with a diverging number of parameters. Science China Mathematic 56,359-377.
[93]Yahav, I. and Shmueli, G. (2009). On Generating Multivariate Poisson Data in Management Science Applications. Applied Stochastic Models in Business and Industry 28,91-102.
[94]Yang, H.M. (2007). Variable selection procedures for generazlied linear mixed models in longitudinal data analysis, Ph.D. Thesis, North Carolina State University.
[95]Yi, G.Y., He, W.Q., and Liang, H. (2009). Analysis of correlated binary data under partially linear single-index logistic models. Journal of Multivariate Analysis 100,278-290.
[96]Yi, G.Y., He, W.Q., and Liang, H. (2011). Semiparametric marginal and association re-gression methods for clustered binary data. Annals of Institute of Statistical Mathematics 63, 511-533.
[97]Yu. Y. and Ruppert, D. (2002). Penalized Spline Estimation for Partially Linear Single-Index Models. Journal of the American Statistical Association 97,1042-1054.
[98]Zhang, C.H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics 38,894-942.
[99]Zhao, S.D. and Li, Y. (2012). Principled sure independence screening for Cox models with ultra-high-dimensional covariates. Journal of Multivariate Analysis 105,397-411.
[100]Zhao, S.D. and Li, Y. (2012). Sure screening for estimating equations in ultra-high dimen-sions. http://arxiv.org/pdf/1110.6817.pdf.
[101]Zhu. L.P.. Li. L.X., Li. R.Z., and Zhu, L.X. (2011). Model-free feature screening for ultrahigh-dimensional data. Journal of the American Statistical Association 106.1464-1475.
[102]Zhu. L.X. and Xue. L.G. (2006). Empirical likelihood confidence regions in a partially linear single-index model. Journal of the Royal Statistical Society, Series B 68,549-570.
[103]Zipunnikov. V.V. and Booth, J.G. (2006). Monte Carlo EM for Generalized Linear Mixed Models using Randomized Spherical Radial Integration, manuscript.
[104]Zou. H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association 101.1418-1429.
[105]Zou, H. and Zhang, H.H. (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics 37,1733-1751.