Jackknifing R-estimators

SUMMARY 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.

[1]  James A. Reeds,et al.  Jackknifing Maximum Likelihood Estimates , 1978 .

[2]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[3]  L. Fernholz.  von Mises Calculus For Statistical Functionals , 1983 .

[4]  J. L. Hodges,et al.  Estimates of Location Based on Rank Tests , 1963 .

[5]  P. Sen.  Some Invariance Principles Relating to Jackknifing and Their Role in Sequential Analysis , 1977 .

[6]  W. Parr.  Jackknifing Differentiable Statistical Functionals , 1985 .

[7]  S. Sheather,et al.  Weighted selectin for the multiset x∓x with application to r–estimates and associated confidence limits , 1989 .

[8]  Hira L. Koul,et al.  An Estimator of the Scale Parameter for the Rank Analysis of Linear Models under General Score Functions , 1987 .

[9]  Tore Schweder,et al.  Window Estimation of the Asymptotic Variance of Rank Estimators of Location. , 1973 .

[10]  Thomas P. Hettmansperger,et al.  Statistical inference based on ranks , 1985 .

[11]  William C. Parr,et al.  Jackknifing L-Statistics with Smooth Weight Functions , 1982 .

[12]  Rupert G. Miller.  The jackknife-a review , 1974 .

[13]  Pranab Kumar Sen.  Functional jackknifing: Rationality and general asymptotics , 1988 .

[14]  J. N. Arvesen.  Jackknifing U-statistics , 1968 .

[15]  C. Frangos.  An updated bibliography on the jackknife method , 1987 .

[16]  S. Sheather.  A new Method of Estimating the Asymptotic Standard Error of the Hodges‐Lehmann Estimator Based on Generalized Least Squares , 1987 .