Thursday, October 22, 2009
04:30 PM in AT UIUC
Professor Guang Cheng
Department of Statistics, Purdue University

Bootstrap Consistency for General Semiparametric M-estimation

Abstract

Consider M-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and a nuisance function parameter. The bootstrap is a widely used resampling method applied to draw inferences in the context of semiparametric M-estimation. We show that, under general conditions, the bootstrap is asymptotically consistent in estimating the distribution of the M-estimate of Euclidean parameter; this is, the bootstrap distribution asymptotically imitates the distribution of the M-estimate. We also show that the bootstrap confidence set has the asymptotically correct coverage probability. These general conclusions hold, in particular, when the nuisance parameter is not estimable at root-n rate. Our results provide a theoretical justification for the use of bootstrap as an inference tool in semiparametric modelling and apply to a broad class of bootstrap methods with exchangeable bootstrap weights. In this paper, we will also apply this general theory to several popular semiparametric models, e.g. Cox regression model with survival data.