Inclusion probabilities proportional to size sampling scheme based on splitting of sizes

Abstract

Srivastava and Singh2 suggested inclusion probabilities proportional to size (IPPS or πPS) sampling scheme which depends upon a specific split of the sizes named as initial split. Each split provides a πPS sampling design with different sets of joint inclusion probabilities (πij ′s). The sampling scheme proposed by them is not exactly πPS unless the largest n units are having same sizes. Furthermore most of the πij′s do not satisfy the condition of non-negativity of variance estimates as suggested by Hanurav1. The scheme has got potential of providing πij ′s satisfying desirable properties with suitable splits; however a systematic approach is needed for getting such splits. Using the information about the nature of non-negativity condition (фij>0) approach, this paper provides split of sizes with less number of trials which gives a set of πij ′s satisfying the condition of non-negativity of variance estimates.