Boostrapping, Jackknife and James-Stein estimators

Abstract

In this article, the most recent results in resampling methods in regression analysis are reviewed. Different classes of estimators are studied and compared the simple "jackknife" the weighted "jackknife" variance estimator for the case of heteroscedastic errors, the variable "jackknife", and the general "bootstrap" estimator. A brief description of Stein-rule estimators in the case of pre-testing estimation then follows. As an application, it is shown how to improve on pre-testing efficiency, following a Stein-rule estimator, by applying bootstrap methods to the estimated variances.