Bootstrap variance and bias estimation in linear models

Abstract

Abstract Let θ be a nonlinear function of the regression parameters and θ be its estimator based on the least‐squares method. This paper studies the bootstrap estimators of the variance and bias of θ. The bootstrap estimators are shown to be consistent and asymptotically unbiased under some conditions. Asymptotic orders of the mean squared errors of the bootstrap estimators are also obtained. The bootstrap and the classical linearization method are compared in a simulation study. Discussions about when to use the bootstrap are given.