Onmout ofnBootstrapping for Nonstandard M-Estimation With Nuisance Parameters

Citations Over TimeTop 19% of 2006 papers

Abstract

Nonstandard 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 L r-type loss functions. We provide empirical evidence using a simulation study to construct confidence intervals and globally estimate sampling distributions. © 2006 American Statistical Association.

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