固定效应部分线性单指数面板模型的快速有效估计及应用
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摘要
将最小二乘支持向量机(LSSVM)和二次推断函数法(QIF)相结合,构造了个体内具有相关结构的固定效应部分线性单指数面板模型的新估计方法;在一定的正则条件下,证明了参数估计量的渐近正态性,导出了非参数估计量的收敛速度;Monte Carlo模拟了所述方法在各种相关结构下的有限样本表现,并与惩罚二次推断函数(PQIF)法进行了比较;将估计技术应用于分析我国人口结构与居民消费率的关系.研究发现,该方法改善了估计量的有效性,应用效果良好,程序运行速度快,适合经济变量间的线性和非线性关系研究以及大数据分析.
By combination of least square vector machine(LSSVM) with quadratic inference functions(QIF),this paper construct a new estimation method for partially linear single index panel model with fixed effects when responses from the same cluster are correlated. Under some regular condition,asymptotic normality of parametric estimators and convergence rate of non-parametric estimator are derived. The finite sample performances of the proposed method are investigated by Monte Carlo simulation under different correlation structures, and compared with penalized quadratic inference functions method(PQIF). The proposed estimation techniques are applied to analyse the relationship between population structure and residents' consumption rate. Our research results show that the efficiency of estimators are improved by the proposed method, application effects are good, program operation has high speed, it is particularly suitable for analysis of linear, nonlinear relationship among economic variables and big data.
By combination of least square vector machine(LSSVM) with quadratic inference functions(QIF),this paper construct a new estimation method for partially linear single index panel model with fixed effects when responses from the same cluster are correlated. Under some regular condition,asymptotic normality of parametric estimators and convergence rate of non-parametric estimator are derived. The finite sample performances of the proposed method are investigated by Monte Carlo simulation under different correlation structures, and compared with penalized quadratic inference functions method(PQIF). The proposed estimation techniques are applied to analyse the relationship between population structure and residents' consumption rate. Our research results show that the efficiency of estimators are improved by the proposed method, application effects are good, program operation has high speed, it is particularly suitable for analysis of linear, nonlinear relationship among economic variables and big data.
引文
[1] Xia Yingcun, Hardle W. Semi-parametric estimation of partially linear single-index Models[J]. Journal of Multivariate Analysis, 2006, 97(5):1162-1184.
[2] Wang Janeling, Xue Liugen, Zhu Lixing, et al. Estimation for a partially linear single index model[J]. The Annals of Statistics, 2010, 38(1):246-274.
[3] Tian Ping, Yang Lin, Xue Liugen. Asymptotic properties of estimators in partially linear single index model for longitudinal data[J]. Acta Mathematica Scientia, 2010, 30(3):677-687.
[4] Jiang Ciren, Wang Janeling. Functional single index models for longitudinal data[J]. The Annals of Statistics, 2011, 39(1):362-388.
[5] Lai Peng, Li Gaorong, Lian Heng. Quadratic inference functions for partially linear singleindex models with longitudinal data[J]. Journal of Multivariate Analysis, 2013, 118(5):115-127.
[6] Chen Jia, Gao Jiti, Li Degui. Estimation in partially linear single-index panel data models with fixed effects[J]. Journal of Business and Economic Statistics, 2013, 31(3):315-330.
[7] Lai Peng, Wang Qihua, Lian Heng. Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data[J]. Journal of Multivariate Analysis, 2012, 105(1):422-432.
[8] Xu Peirong, Zhu Lixing. Estimation for a marginal generalized single-index longitudinal model[J]. Journal of Multivariate Analysis, 2012, 105(1):285-299.
[9] Qu Annie, Lindsay B G, Li Bing. Improving generalised estimating equations using quadratic inference functions[J]. Biometrika, 2000, 87(4):823-836.
[10] Bai Yang, Fung W K, Zhu Zhongyi. Penalized quadratic inference functions for single-index models with longitudinal data[J]. Journal of Multivariate Analysis, 2009, 100(1):152-161.
[11] Li Gaorong, Lai Peng, Lian Heng. Variable selection and estimation for partially linear single-index models with longitudinal data[J]. Statistics and Computing, 2014, 25(3):579-593.
[12]邓乃扬,田英杰.数据挖掘中的新方法-支持向量机[M].北京:科学出版社,2004.
[13] Suykens J A K, Vandewalle J. Least squares support vector machine classifiers[J]. Neural Processing Letters, 1999, 9(3):293-300.
[14] Shim J, Hwang C, Jeong S, et al. Varying coefficient modeling via least square support vector regression[J]. Neurocomputing, 2015, 161:254-259.
[15] Chen Chuanfa, Yan Changqing, Li Yanyan. A robust weighted least squares support vector regression based on least trimmed squares[J]. Neurocomputing, 2015, 168:941-946.
[16] Suykens J A K, Gestel T V, Brabanter J D, et al. Least Square Support Vector Machines[M].Singapore:World Scientific Publishing Co. Pte. Ltd, 2002.
[17] Koenker R. Quantile Regression[M]. London:Cambridge University Press, 2005.
[18] Golub G H, Health M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter[J]. Technometrics, 1979, 21(2):215-223.
[19] Ruppert D, Wand M P, Carroll R J. Semiparametric Regression[M]. London:Cambridge University, 2003.
[20] He Xuming,Fung W K,Zhu Zhongyi. Robust estimation in generalized partial linear models for clustered data[J]. Journal of the American Statistical Association, 2005, 100(472):1176-1184.
[2] Wang Janeling, Xue Liugen, Zhu Lixing, et al. Estimation for a partially linear single index model[J]. The Annals of Statistics, 2010, 38(1):246-274.
[3] Tian Ping, Yang Lin, Xue Liugen. Asymptotic properties of estimators in partially linear single index model for longitudinal data[J]. Acta Mathematica Scientia, 2010, 30(3):677-687.
[4] Jiang Ciren, Wang Janeling. Functional single index models for longitudinal data[J]. The Annals of Statistics, 2011, 39(1):362-388.
[5] Lai Peng, Li Gaorong, Lian Heng. Quadratic inference functions for partially linear singleindex models with longitudinal data[J]. Journal of Multivariate Analysis, 2013, 118(5):115-127.
[6] Chen Jia, Gao Jiti, Li Degui. Estimation in partially linear single-index panel data models with fixed effects[J]. Journal of Business and Economic Statistics, 2013, 31(3):315-330.
[7] Lai Peng, Wang Qihua, Lian Heng. Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data[J]. Journal of Multivariate Analysis, 2012, 105(1):422-432.
[8] Xu Peirong, Zhu Lixing. Estimation for a marginal generalized single-index longitudinal model[J]. Journal of Multivariate Analysis, 2012, 105(1):285-299.
[9] Qu Annie, Lindsay B G, Li Bing. Improving generalised estimating equations using quadratic inference functions[J]. Biometrika, 2000, 87(4):823-836.
[10] Bai Yang, Fung W K, Zhu Zhongyi. Penalized quadratic inference functions for single-index models with longitudinal data[J]. Journal of Multivariate Analysis, 2009, 100(1):152-161.
[11] Li Gaorong, Lai Peng, Lian Heng. Variable selection and estimation for partially linear single-index models with longitudinal data[J]. Statistics and Computing, 2014, 25(3):579-593.
[12]邓乃扬,田英杰.数据挖掘中的新方法-支持向量机[M].北京:科学出版社,2004.
[13] Suykens J A K, Vandewalle J. Least squares support vector machine classifiers[J]. Neural Processing Letters, 1999, 9(3):293-300.
[14] Shim J, Hwang C, Jeong S, et al. Varying coefficient modeling via least square support vector regression[J]. Neurocomputing, 2015, 161:254-259.
[15] Chen Chuanfa, Yan Changqing, Li Yanyan. A robust weighted least squares support vector regression based on least trimmed squares[J]. Neurocomputing, 2015, 168:941-946.
[16] Suykens J A K, Gestel T V, Brabanter J D, et al. Least Square Support Vector Machines[M].Singapore:World Scientific Publishing Co. Pte. Ltd, 2002.
[17] Koenker R. Quantile Regression[M]. London:Cambridge University Press, 2005.
[18] Golub G H, Health M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter[J]. Technometrics, 1979, 21(2):215-223.
[19] Ruppert D, Wand M P, Carroll R J. Semiparametric Regression[M]. London:Cambridge University, 2003.
[20] He Xuming,Fung W K,Zhu Zhongyi. Robust estimation in generalized partial linear models for clustered data[J]. Journal of the American Statistical Association, 2005, 100(472):1176-1184.