On a class of congruent sample design and their properties

Abstract

As is known in sampling with unequal probabilities without replacement the efficiency of the Horvitz-Thompson estimator may happen to be a decreasing function of the sample size (unlike in simple random sampling). In this paper sufficient conditions are given to ensure that the efficiency will increase monotonically with sample size. Such conditions lead to the definition of families of sample designs qualified as "congruent". among these, there is a generalization of the design due to Lahiri.