Jackknife variance estimation for general two-sample statistics and applications to common mean estimators under ordered variances

Abstract

We study the jackknife variance estimator for a general class of two-sample statistics. As a concrete application, we consider samples with a common mean but possibly different, ordered variances as arising in various fields such as interlaboratory experiments, field studies, or the analysis of sensor data. Estimators for the common mean under ordered variances typically employ random weights, which depend on the sample means and the unbiased variance estimators. They take different forms when the sample estimators are in agreement with the order constraints or not, which complicates even basic analyses such as estimating their variance. We propose to use the jackknife, whose consistency is established for general smooth two-sample statistics induced by continuously Gâteux or Frechet-differentiable functionals, and, more generally, asymptotically linear two-sample statistics, allowing us to study a large class of common mean estimators. Furthermore, it is shown that the common mean estimators under consideration satisfy a central limit theorem (CLT). We investigate the accuracy of the resulting confidence intervals by simulations and illustrate the approach by analyzing several data sets.