Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24169
Title: On locally weighted estimation and hypothesis testing of varying-coefficient models with missing covariates
Authors: Wong, H 
Guo, S
Chen, M
Ip, WC
Keywords: Local linear smoother
Locally weighted estimating equation
Missing at random
Varying-coefficient models
Issue Date: 2009
Publisher: Elsevier Science Bv
Source: Journal of statistical planning and inference, 2009, v. 139, no. 9, p. 2933-2951 How to cite?
Journal: Journal of Statistical Planning and Inference 
Abstract: Varying-coefficient model Y = ∑j = 1 p βj (U) Xj + ε 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 over(β, ^) (·) is derived when the selection probabilities are known, estimated parametrically or nonparametrically. We show that the resulting nonparametric estimator of over(β, ^) (·) 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.
URI: http://hdl.handle.net/10397/24169
DOI: 10.1016/j.jspi.2009.01.016
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