Reducing component estimation for varying coefficient models with longitudinal data  

作　　者：TANG QingGuo~(1,2+) WANG JinDe~2 1 Institute of Sciences,People’s Liberation Army University of Science and Technology,Nanjing 210007,China 2 Department of Mathematics,Nanjing University,Nanjing 210093,China 

出　　处：《Science China Mathematics》2008年第2期250-272,共23页中国科学：数学（英文版）

基　　金：Research Foundation for Doctor Programme (Grant No.20060254006);the National Natural Science Foundation of China (Grant No.10671089)

摘　　要：Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields. In this paper, a reducing component procedure is proposed for estimating the unknown functions and their derivatives in very general models, in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time-dependent. The asymptotic properties of the estimators, such as consistency, rate of convergence and asymptotic distribution, are derived. The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness. Finite sample properties of our procedures are studied through Monte Carlo simulations.

关 键 词：varying coefficient model longitudinal data nonparametric estimation reducing component estimators asymptotic normality 62G07 

分 类 号：O211[理学—概率论与数理统计]