On m out of n bootstrapping for nonstandard M-estimation with nuisance parameters
成果类型：
Article
署名作者：
Lee, Stephen M. S.; Pun, M. C.
署名单位：
University of Hong Kong
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214506000000014
发表日期：
2006
页码：
1185-1197
关键词：
摘要：
Nonstandard M-estimation, with nuisance parameters consistently estimated in the criterion function, often yields M-estimators converging weakly at rates different from n(1/2) with weak limits that are typically non-Gaussian. The complicated asymptotics involved makes distributional estimation of the M-estimators analytically prohibitive. We show that the problem is resolved by m out of n bootstrapping under very general conditions, which provides a universal and convenient approach to consistently estimating sampling distributions of M-estimators. We illustrate our findings with applications to least median of squares regression estimators, studentized location M-estimators, shorth estimators, and robust M-estimators derived from L-r-type loss functions. We provide empirical evidence using a simulation study to construct confidence intervals and globally estimate sampling distributions.