BEHAVIOUR OF JACKKNIFE ESTIMATORS IN TERMS OF ASYMPTOTIC DEFICIENCY UNDER TRUE AND ASSUMED MODELS

Dedicated to Professor Yukihiro Kodama on his 60th birthday

Abstract

The problem on jackknifing estimators is investigated in the presence of nuisance parameters from the viewpoint of higher order asymptotics. It is shown that the asymptotic deficiency of the jackknife estimator relative to the bias-adjusted maximum likelihood estimator (MLE) is equal to zero under true and assumed models. Moreover, the asymptotic deficiency of the MLE or the jackknife estimator under the assumed model relative to that under the true model is given.