Approximating the Distribution of M-Estimators in Linear Models by Randomly Weighted Bootstrap
线性模型中M估计分布的随机加权方法逼近

The asymptotic distribution of the M-estimators are generally related to quantities of the error distribution that can not be conveniently estimated. The randomly weighted bootstrap method provides a way of assessing the distribution of theM-estimators without estimating the nuisance quantities of the error distributions. In this paper, the distribution of M-estimators is approximated by the randomly weighted bootstrap method in linear models when the covariates are random. It is shown that the randomly weighted bootstrapping estimation of the distribution of the M-estimator is uniformly consistent. Also, the variance estimates is investigated by Monte Carlo simulations for different choices of the convex function, sample size and random weights. Poisson weighting is recommended for reducing the computational burden in the randomly weighted bootstrapping M-estimators.