On a family of sampling schemes with inclusion probability proportional to size

Abstract

A family of sampling schemes with inclusion probability proportional to size is proposed. The schemes are based upon certain combinatorial properties of balanced incomplete block designs and are available for any sample size. Schemes belonging to this family are satisfactory from the point of view of (i) simplicity in selection, (ii) availability of an unbiased variance estimator and (iii) precision of the estimate. The efficiency has been compared empirically with that of some well-known sampling schemes.