JACKKNIFING IN THE PRESENCE OF INHOMOGENEITY

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