In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistic...In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.展开更多
In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be est...In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.展开更多
In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average varianc...In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.展开更多
部分线性单指标模型是在科学研究中具有广泛应用的经典半参数模型之一.本文主要研究具有自相关误差结构的面板数据的部分线性单指标模型的统计推断问题.通过结合局部多项式和纠偏广义估计方程方法,本文提出模型参数的可行加权广义估计(f...部分线性单指标模型是在科学研究中具有广泛应用的经典半参数模型之一.本文主要研究具有自相关误差结构的面板数据的部分线性单指标模型的统计推断问题.通过结合局部多项式和纠偏广义估计方程方法,本文提出模型参数的可行加权广义估计(feasible weighted generalized estimating equation estimation, GEE-FW),证明该估计具有相合性和渐近正态性,并且在渐近方差意义下阐明该估计比工作独立的广义估计(generalized estimating equation estimation based on working independence,GEE-WI)更加有效.此外,本文对模型中未知连接函数提出两阶段局部线性估计(two step local linear generalized estimating equation estimation, GEE-TS),建立该估计的渐近性质.数值模拟研究和实际数据分析都表明了本文所提出的方法是有效的,在理论和应用方面均具有良好的表现.展开更多
基金supported by the Natural Science Foundation of Beijing City(Grant No.1042002)Technology Development Plan Project of Beijing Education Committee(Grant No.KM2005 10005009)+1 种基金the Special Grants of Beijing for Talents(Grant No.20041D0501515)supported by a grant from the Research Grants Council of Hong Kong,Hong Kong(Grant No.HKU7060/04P).
文摘In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.
基金Supported by the National Natural Science Foundation of China (10571008)the Natural Science Foundation of Henan (092300410149)the Core Teacher Foundationof Henan (2006141)
文摘In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.
文摘In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.
文摘部分线性单指标模型是在科学研究中具有广泛应用的经典半参数模型之一.本文主要研究具有自相关误差结构的面板数据的部分线性单指标模型的统计推断问题.通过结合局部多项式和纠偏广义估计方程方法,本文提出模型参数的可行加权广义估计(feasible weighted generalized estimating equation estimation, GEE-FW),证明该估计具有相合性和渐近正态性,并且在渐近方差意义下阐明该估计比工作独立的广义估计(generalized estimating equation estimation based on working independence,GEE-WI)更加有效.此外,本文对模型中未知连接函数提出两阶段局部线性估计(two step local linear generalized estimating equation estimation, GEE-TS),建立该估计的渐近性质.数值模拟研究和实际数据分析都表明了本文所提出的方法是有效的,在理论和应用方面均具有良好的表现.
