Estimation of Semi-Varying Coefficient Model with Surrogate Data and Validation Sampling  

作　　者：Ya-zhao L Ri-quan ZHANG Zhen-sheng HUANG 

机构地区：[1]Department of Statistics,East China Normal University [2]Institute of Operational Research and Cybernetics,Hangzhou Dianzi University [3]Department of Mathematics,Shanxi Datong University [4]School of Science,Nanjing University of Science and Technology

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第3期645-660,共16页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10871072,11171112 and 11101114);the Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y201121276);the Doctoral Fund of Ministry of Education of China(200900076110001)

摘　　要：In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate. Data-driven bandwidth selection methods are also discussed. Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate. Data-driven bandwidth selection methods are also discussed. Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.

关 键 词：asymptotic normality profile likelihood measurement error validation sampling semi-varying coefficient model 

分 类 号：O212.1[理学—概率论与数理统计]