Efficiency and robustness of a resampling M-estimator in the linear model

In the literature, there are basically two kinds of resampling methods for least squares estimation in linear models; the E-type (the efficient ones l ike the classical bootstrap), which is more efficient when error variables are homogeneous, and the R-type (the robust ones like the jackknife), which is more robust for heterogeneous errors. However, for M-estimation of a li near model, we Find a counterexample showing that a usually E-type method i s less efficient than an R-type method when error variables are homogeneous . In this paper, we give sufficient conditions under which the classificati on of the two types of the resampling methods is still true. (C) 2001 Acade mic Press.