Weighted estimation of single index models with right censored responses  

作　　者：WANG YanHua1, LI XiaYan2, WANG QiHua3 & HE ShuYuan4 1School of Sciences, Beijing Institute of Technology, Beijing 100081, China 2Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 3Chinese Academy of Mathematics and System Science, Beijing 100080, China 4School of Mathematical Sciences, Capital Normal University, Beijing 100048, China 

出　　处：《Science China Mathematics》2011年第3期479-514,共36页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10731010, 10971012 and 11071015)

摘　　要：In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

关 键 词：single index models random censorship central limit theorem law of the iterated logarithm weighted least squares unknown link function 

分 类 号：O211.4[理学—概率论与数理统计]