Estimation for Partially Linear Models with Missing Responses:the Fixed Design Case  

作　　者：Yong-song QIN Ying-hua LI 

机构地区：[1]School of Mathematics and Statistics,Guangxi Normal University Guilin

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第2期447-472,共26页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11271088,11361011,11201088);Guangxi"Bagui Scholar"Special Project Foundation;the Natural Science Foundation of Guangxi(No.2013GXNS-FAA019004,2013GXNSFAA019007,2013GXNSFBA019001)

摘　　要：Suppose that we have a partially linear model Yi = xiβ ＋ g（ti） ＋εi with independent zero mean errors εi, where （xi,ti, i = 1, ... ,n} are non-random and observed completely and （Yi, i = 1,...,n} are missing at random（MAR）. Two types of estimators of β and g（t） for fixed t are investigated： estimators based on semiparametric regression and inverse probability weighted imputations. Asymptotic normality of the estimators is established, which is used to construct normal approximation based confidence intervals on β and g（t）. Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.Suppose that we have a partially linear model Yi = xiβ ＋ g（ti） ＋εi with independent zero mean errors εi, where （xi,ti, i = 1, ... ,n} are non-random and observed completely and （Yi, i = 1,...,n} are missing at random（MAR）. Two types of estimators of β and g（t） for fixed t are investigated： estimators based on semiparametric regression and inverse probability weighted imputations. Asymptotic normality of the estimators is established, which is used to construct normal approximation based confidence intervals on β and g（t）. Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.

关 键 词：partially linear model fixed design point missing at random confidence interval 

分 类 号：O212[理学—概率论与数理统计]