Title: On<i>m</i>out of<i>n</i>Bootstrapping for Nonstandard M-Estimation With Nuisance Parameters
Abstract: AbstractNonstandard M-estimation, with nuisance parameters consistently estimated in the criterion function, often yields M-estimators converging weakly at rates different from n1/2 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 Lr-type loss functions. We provide empirical evidence using a simulation study to construct confidence intervals and globally estimate sampling distributions.KEY WORDS: Gaussian processm out of n bootstrapM-estimatorNuisance parameterSubsampling
Publication Year: 2006
Publication Date: 2006-09-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 44
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