基于sieve方法的响应变量为当前状态数据的部分函数型线性模型的估计
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摘要
利用sieve方法研究响应变量为当前状态数据的部分函数型线性模型的估计.在一定的条件下,证明了该估计的强相合性和渐近正态性,得到了该估计的收敛速度,并且非参数部分达到最优收敛速度.最后通过一个数值模拟来研究该估计的有限样本性质.
In this paper, sieve method is used to obtain the estimators for partial functional linear model with current status data. Under some mild conditions, the estimators are proved to be strong consistent and asymptotically normally distributed, and the convergence rate of the estimators is obtained and the nonparametric part of the estimators has an optimal convergence rate. Finally, a simulation study is carried out to illustrate the finite sample properties of our proposed estimators.
In this paper, sieve method is used to obtain the estimators for partial functional linear model with current status data. Under some mild conditions, the estimators are proved to be strong consistent and asymptotically normally distributed, and the convergence rate of the estimators is obtained and the nonparametric part of the estimators has an optimal convergence rate. Finally, a simulation study is carried out to illustrate the finite sample properties of our proposed estimators.
引文
[1] Ma Haiqiang, Bai Yang, Zhu Zhongyi. Dynamic single-index model for functional data[J].Science China Mathematics, 2016, 59(12):2561-2584.
[2] Ma Haiqiang, Zhu Zhongyi. Continuously dynamic additive models for functional data[J].Journal of Multivariate Analysis, 2016, 150:1-13.
[3] Zhou Jian.jun, Chen Min. Spline estimators for semi-functional linear model[J], Statistics&Probability Letters, 2012, 82(3):505-513.
[4] Huang Lele, Wang Huiwen, Cui Hengjian, et al. Sieve M-estimator for a semi-functional linear model[J]. Science China Mathematics, 2015, 58(11):2421-2434.
[5] Lu Ying, Du Jiang, Sun Zhimeng. Functional partially linear quantile regression model[J].Metrika, 2014, 77(2):317-332.
[6] Hall P, Horowitz J L. Methodology and convergence rates for functional linear regression[J].The Annals of Statistics, 2007, 35(1):70-91.
[7] Fan Jianqing, Zhang Jinting. Two-step estimation of functional linear models with applications to longitudinal data[J]. Journal of the Royal Statistical Society:Series B(Statistical Methodology), 2000, 62(2):303-322.
[8] Cardot H, Ferraty F, Sarda P. Spline estimators for the functional linear model[J]. Statistica Sinica, 2007, 13(3):571-591.
[9] Ramsay J O, Silverman B W. Functional data analysis[M]. Springer, New York, 1997.
[10] Shin H. Partial functional linear regression[J]. Journal of Statistical Planning and Inference2009, 139(10):3405-3418.
[11] Sun Jianguo, Sun Liuquan. Semiparametric linear transformation models for current status data[J]. Canadian Journal of Statistics, 2005, 33:85-96.
[12] Zhang Zhigang, Sun Jianguo, Sun Liuquan. Statistical analysis of current status data with informative observation times[J]. Statistics in Medicine, 2005, 24:1399-1407.
[13] Zhang Bin, Tong Xingwei, Zhang Jing et al. Efficient estimation for linear transformation models with current status data[J]. Communications in Statistics-Theory and Methods, 2013,42(17):3191-3203.
[14] Huang Jian. Efficient estimation for the proportional hazards model with interval censoring[J]. The Annals of Statistics, 1996, 24:540-568.
[15] Huang Jian, Rossini A J. Sieve estimation for the proportional odds failure-time regression model with interval censoring[J]. Journal of the American Statistical Association, 1997, 92:960-967.
[16] Li Gang, Zhang Cunhui. Linear regression with interval censored data[J]. The Annals of Statistics, 1998, 26:1306-1327.
[17] Lin D Y, Oakes D, Ying Z. Additive hazards regression with current status data[J].Biometrika, 1998, 85:289-298.
[18] Schumaker L L. Spline functions:basic theory[M]. New York:Wiley, 1981.
[19] Xue Hongqi, Lam K F, Li Gongying. Sieve maximum likelihood estimator for semiparametric regression models with current status data[J]. Journal of the American Statistical Association, 2004, 99(466):346-357.
[20] Peng Hanxiang. Efficient inference in a semiparametric generalized linear model[J]. Journal of Nonparametric Statistics, 2008, 20(2):115-127.
[21] Chen Hung. Polynomial splines and nonparametric regression[J]. Journal of Nonparametric Statistics, 1991, 1(1-2):143-156.
[22] De Boor C. A practical guide to splines[M]. New York:Springer Verlag, 1978.
[23] Shen Xiaotong, Wong Winghung. Convergence rate of sieve estimates[J]. Annals of Statistics,1994, 22(2):580-615.
[24] Yu Ping, Du Jiang, Zhang Zhongzhan. Single-index partially functional linear regression model[J]. Statistical Papers, 2018(11):1-17.
[2] Ma Haiqiang, Zhu Zhongyi. Continuously dynamic additive models for functional data[J].Journal of Multivariate Analysis, 2016, 150:1-13.
[3] Zhou Jian.jun, Chen Min. Spline estimators for semi-functional linear model[J], Statistics&Probability Letters, 2012, 82(3):505-513.
[4] Huang Lele, Wang Huiwen, Cui Hengjian, et al. Sieve M-estimator for a semi-functional linear model[J]. Science China Mathematics, 2015, 58(11):2421-2434.
[5] Lu Ying, Du Jiang, Sun Zhimeng. Functional partially linear quantile regression model[J].Metrika, 2014, 77(2):317-332.
[6] Hall P, Horowitz J L. Methodology and convergence rates for functional linear regression[J].The Annals of Statistics, 2007, 35(1):70-91.
[7] Fan Jianqing, Zhang Jinting. Two-step estimation of functional linear models with applications to longitudinal data[J]. Journal of the Royal Statistical Society:Series B(Statistical Methodology), 2000, 62(2):303-322.
[8] Cardot H, Ferraty F, Sarda P. Spline estimators for the functional linear model[J]. Statistica Sinica, 2007, 13(3):571-591.
[9] Ramsay J O, Silverman B W. Functional data analysis[M]. Springer, New York, 1997.
[10] Shin H. Partial functional linear regression[J]. Journal of Statistical Planning and Inference2009, 139(10):3405-3418.
[11] Sun Jianguo, Sun Liuquan. Semiparametric linear transformation models for current status data[J]. Canadian Journal of Statistics, 2005, 33:85-96.
[12] Zhang Zhigang, Sun Jianguo, Sun Liuquan. Statistical analysis of current status data with informative observation times[J]. Statistics in Medicine, 2005, 24:1399-1407.
[13] Zhang Bin, Tong Xingwei, Zhang Jing et al. Efficient estimation for linear transformation models with current status data[J]. Communications in Statistics-Theory and Methods, 2013,42(17):3191-3203.
[14] Huang Jian. Efficient estimation for the proportional hazards model with interval censoring[J]. The Annals of Statistics, 1996, 24:540-568.
[15] Huang Jian, Rossini A J. Sieve estimation for the proportional odds failure-time regression model with interval censoring[J]. Journal of the American Statistical Association, 1997, 92:960-967.
[16] Li Gang, Zhang Cunhui. Linear regression with interval censored data[J]. The Annals of Statistics, 1998, 26:1306-1327.
[17] Lin D Y, Oakes D, Ying Z. Additive hazards regression with current status data[J].Biometrika, 1998, 85:289-298.
[18] Schumaker L L. Spline functions:basic theory[M]. New York:Wiley, 1981.
[19] Xue Hongqi, Lam K F, Li Gongying. Sieve maximum likelihood estimator for semiparametric regression models with current status data[J]. Journal of the American Statistical Association, 2004, 99(466):346-357.
[20] Peng Hanxiang. Efficient inference in a semiparametric generalized linear model[J]. Journal of Nonparametric Statistics, 2008, 20(2):115-127.
[21] Chen Hung. Polynomial splines and nonparametric regression[J]. Journal of Nonparametric Statistics, 1991, 1(1-2):143-156.
[22] De Boor C. A practical guide to splines[M]. New York:Springer Verlag, 1978.
[23] Shen Xiaotong, Wong Winghung. Convergence rate of sieve estimates[J]. Annals of Statistics,1994, 22(2):580-615.
[24] Yu Ping, Du Jiang, Zhang Zhongzhan. Single-index partially functional linear regression model[J]. Statistical Papers, 2018(11):1-17.