Efficiency and Robustness in Resampling

Abstract

It is known that the standard delete-1 jackknife and the classical bootstrap are in general equally efficient for estimating the mean-square-error of a statistic in the i.i.d. setting. However, this equivalence no longer holds in the linear regression model. It turns out that the bootstrap is more efficient when error variables are homogeneous and the jackknife is more robust when they are heterogeneous. In fact, we can divide all the commonly used resampling procedures for linear regression models into two types: the E-type (the efficient ones like the bootstrap) and the R-type (the robust ones like the jackknife). Thus the theory presented here provides a unified view of all the known resampling procedures in linear regression.