Comparing the Positive Jackknife with the Usual Jackknife

Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

The positive jackknife is a variant of the familiar jackknife technique which also provides estimators of bias and variance for a wide class of statistics. The techniques are first-order equivalent. Using asymptotic expansions, a second-order bias comparison is performed for both biases and variance estimators. This analysis provides guidelines for describing when one technique might be preferred. The guidelines are difficult to explicitly evaluate for statistics based on continuous random variable but are often simple for categorical data situations. Examples are considered together with some small-sample calculations to evaluate the applicability of the asymptotic results for small samples.