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Semiparametric regression analysis with missing response at random

Authors: Wolfgang Härdle , Oliver Linton and Wang, Qihua
Date: 01 April 2003
Type: cemmap Working Paper, CWP11/03
DOI: 10.1920/wp.cem.2003.1103

Abstract

We develop inference tools in a semiparametric partially linear regression model with missing response data. A class of estimators is defined that includes as special cases: a semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal.

The three special estimators have the same asymptotic variance. They achieve the semiparametric efficiency bound in the homoskedastic Gaussian case. We show that the Jackknife method can be used to consistently estimate the asymptotic variance. Our model and estimators are defined with a view to avoid the curse of dimensionality, that severely limits the applicability of existing methods. The empirical likelihood method is developed. It is shown

that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable. An adjusted empirical log-likelihood ratio, which is asymptotically

standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the adjusted and bootstrap empirical likelihood with the normal approximation

based method in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also

made by simulation between the proposed estimators and the related estimators.

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Now published:
Wang, Qihua, Oliver Linton and Wolfgang Härdle December 2004, Semiparametric regression analysis with missing response at random, Journal Article, Taylor & Francis

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