Open Access
October 2009 Estimating linear functionals in nonlinear regression with responses missing at random
Ursula U. Müller
Ann. Statist. 37(5A): 2245-2277 (October 2009). DOI: 10.1214/08-AOS642


We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be “missing at random.” We assume that the errors have mean zero and are independent of the covariates. In order to estimate expectations of functions of covariate and response we use a fully imputed estimator, namely an empirical estimator based on estimators of conditional expectations given the covariate. We exploit the independence of covariates and errors by writing the conditional expectations as unconditional expectations, which can now be estimated by empirical plug-in estimators. The mean zero constraint on the error distribution is exploited by adding suitable residual-based weights. We prove that the estimator is efficient (in the sense of Hájek and Le Cam) if an efficient estimator of the parameter is used. Our results give rise to new efficient estimators of smooth transformations of expectations. Estimation of the mean response is discussed as a special (degenerate) case.


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Ursula U. Müller. "Estimating linear functionals in nonlinear regression with responses missing at random." Ann. Statist. 37 (5A) 2245 - 2277, October 2009.


Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62052
MathSciNet: MR2543691
Digital Object Identifier: 10.1214/08-AOS642

Primary: 62J02
Secondary: 62F12 , 62G20 , 62N01

Keywords: Confidence interval , empirical likelihood , gradient , influence function , semiparametric regression , weighted empirical estimator

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5A • October 2009
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