Properties and Modifications of a Probability Proportional to Size Sampling Procedure

There are numerous procedures for selecting a sample PPS without replacement. Brewer and Hanif (1983) discuss the properties of 50 such procedures. One of the more interesting of these procedures originally appeared in Jessen (1969). This procedure possesses several desirable properties including: relative simplicity of sample selection, fixed sample size of any desired size, selection strictly PPS without replacement, unbiased estimators of variance, and simple calculation of joint inclusion probabilities. In this paper we study possible modifications of Jessen’s procedure to obtain two other desirable properties, namely: (1) how to obtain a sample expansion with the expanded sample remaining PPS without replacement; and (2) how to adjust the joint selection probabilities in order to exclude the possibility of negative variance estimates when using the Yates-Grundy variance estimator