Richardson extrapolation and the bootstrap

Abstract

SUMMARY. The m out of n bootstrap, with or without replacement, where m→∞ and m/n → 0 has been proposed on two grounds: (i) As a way of ensuring consistency when the classical bootstrap is not consistent. (ii) When it is consistent, then in conjunction with extrapolation, as a way of obtaining behaviour equivalent to that of the classical bootstrap, to second or higher order, with reduced computation time. In this paper we shall discuss a partial taxonomy of higher order behaviour of the m out of n bootstrap and introduce a general form of extrapolation. 1