ESTIMATING LINEAR FUNCTIONALS IN NONLINEAR REGRESSION WITH RESPONSES MISSING AT RANDOM

• 成果类型: Article
• 署名作者: Mueller, Ursula U.
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS642
• 发表日期: 2009
• 页码: 2245-2277
• 关键词: likelihood-based inference; empirical-likelihood; efficient estimation; mean functionals; models; imputation

摘要

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 all empirical estimator based oil estimators of conditional expectations given the covariate. We exploit the independence of covariates and errors by writing the conditional expectations as unconditional expectations, which call now be estimated by empirical plug-in estimators. The mean zero constraint oil the error distribution is exploited by adding Suitable residual-based weights. We prove that the estimator is efficient (in the sense of Hajek 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.