Inference on Varying-Coefficient Partially Linear Regression Model  

作　　者：Jing-yan FENG Ri-quan ZHANG Yi-qiang LU 

机构地区：[1]Department of Mathematics, Shanxi Datong University [2]Department of Statistics, East China Normal University [3]Institute of Electronic Technology, the PLA Information Engineering University

出　　处：《Acta Mathematicae Applicatae Sinica》2015年第1期139-156,共18页应用数学学报（英文版）

基　　金：supported in part by National Natural Science Foundation of China(11171112,11201190);Doctoral Fund of Ministry of Education of China(20130076110004);Program of Shanghai Subject Chief Scientist(14XD1401600);the 111 Project of China(B14019)

摘　　要：The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.

关 键 词：asymptotic normality varying-coefficient partially linear regression model generalized likelihoodratio test Wilks phenomenon xi-distribution. 

分 类 号：O212.1[理学—概率论与数理统计]