Horvitz-Thompson variance weights

Abstract

Sequential probability minimum replacement sample designs provide a practical methodology for selecting PPS samples that satisfy the requirement of positive pairwise probabilities and nonnegative variance weights. The exact solutions for the variance weights can lead to some unacceptable variance estimates such as zero estimates regardless of the observed values. This paper explores some alternative approximate variance estimators that avoid this problem. Although not strictly unbiased, the variance estimates from alternate estimators can be shown to be nearly unbiased and to have less variability than the unbiased variance estimators based on the exact variance weights. Some comparisons to PPS systematic designs are also addressed with alternate variance weights.