On locally weighted estimation and hypothesis testing of varying-coefficient models with missing covariates

doi:10.1016/j.jspi.2009.01.016

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	On locally weighted estimation and hypothesis testing of varying-coefficient models with missing covariates
	Wong, Heung 2; Guo, Shaojun 1; Chen, Min1 ; Ip, Wai-Cheung 2
	2009-09-01
发表期刊	JOURNAL OF STATISTICAL PLANNING AND INFERENCE
ISSN	0378-3758
卷号	139 期号:9 页码:2933-2951
摘要	Varying-coefficient model Y = Sigma(p)(j=1) beta(j)(U)X-j+epsilon has been studied extensively when data are completely observed. When the covariates X are missing at random, we propose a locally weighted estimator based on the inverse selection probabilities. Distribution theory of (beta) over cap(center dot) is derived when the selection probabilities are known, estimated parametrically or nonparametrically. We show that the resulting nonparametric estimator of (beta) over cap(center dot) when the selection probabilities are estimated nonparametrically has a smaller asymptotic variance than that when the selection probabilities are known or estimated parametrically. Motivated by Robin et al. [1994. Estimation of regression coefficients when some regressors are not always observed. J. Amer. Statist. Assoc. 89, 846-866], we also consider simple locally augmented weighted estimator. However, we show that it does not improve the efficiency theoretically. We have constructed a bootstrap test for goodness of fit of models in the missing covariates case. The results of a simulation study are also given to illustrate our method. The proposed method is applied to analyze an AIDS dataset from a clinical study. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.
关键词	Varying-coefficient models Local linear smoother Locally weighted estimating equation Missing at random
DOI	10.1016/j.jspi.2009.01.016
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000267956600007
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8827
专题	应用数学研究所
通讯作者	Guo, Shaojun
作者单位	1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Wong, Heung,Guo, Shaojun,Chen, Min,et al. On locally weighted estimation and hypothesis testing of varying-coefficient models with missing covariates[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE,2009,139(9):2933-2951.
APA	Wong, Heung,Guo, Shaojun,Chen, Min,&Ip, Wai-Cheung.(2009).On locally weighted estimation and hypothesis testing of varying-coefficient models with missing covariates.JOURNAL OF STATISTICAL PLANNING AND INFERENCE,139(9),2933-2951.
MLA	Wong, Heung,et al."On locally weighted estimation and hypothesis testing of varying-coefficient models with missing covariates".JOURNAL OF STATISTICAL PLANNING AND INFERENCE 139.9(2009):2933-2951.