Sufficiency in Sampling Theory

Abstract

The present paper is an attempt to define sufficiency in simple terms in the theory of sampling. This definition is a suitable version of the existing notion of sufficiency as defined by Fisher, Halmos and Savage, Bahadur and others. The paper gives justification for the use of sufficient statistics in sampling theory. Applications to interpenetrating subsampling and two-stage sampling are given. In interpenetrating subsampling, it is proved that for estimating the population mean when the subsamples are drawn by simple random sampling without replacement, an estimator better than the usual overall average of subsample means is given by the average of distinct sample units. An improved estimator of the population variance is derived. In two-stage sampling where the first-stage units are drawn with unequal probabilities and second-stage units by simple random sampling (without replacement), two estimators of the population mean which are better than the estimator in current use are given.