Jackknifing in the presence of inhomogeneity
Under the classical assumption that data are a random sample from a distribution with cumulative distribution function F, the jackknife generally yields bias reduction, an (asymptotically) pivotal statistic, and a variance estimator for an estimator of an unknown parameter. In this article, the classical assumption is relaxed to allow for inhomogeneous subpopulations. The jackknife is seen to account for these inhomogeneities automatically and, so, is valid in a class of problems much larger than that for which it was originally intended. Data from experiments to determine the acceleration of gravity at Washington, D.C., are analyzed. A family of weighted-mean estimators is considered, and recommendations are made regarding which estimators yield both valid and efficient jackknife-based inferences.