Jackknifing R-estimators

Abstract

Sufficient conditions are given for the consistency of the jackknife variance estimator for R -estimators of location in the one- and two-sample problems. In particular, the jackknife is shown to produce strongly consistent estimates of the variance of the Hodges–Lehmann estimator. An efficient algorithm for computing the variance estimator is presented. For the two sample sizes considered in this paper, calculations for the jackknife estimator of the variance of the Hodges–Lehmann estimator are about 50 times as fast as the bootstrap variance estimator with B = 100. Some Monte Carlo evidence of the small-sample efficiency of this jackknife variance estimator is reported. Extensions of the results to R -estimators in the linear model context are discussed.