A New Variance Estimator for a Two‐phased Restratified Sample with PPS Sampling at Both Phases

Suojin Wang, Alan H. Dorfman, and Lawrence R. Ernst


In this paper we consider variance estimation for population totals and ratios in complex, cross stratified surveys in which the ultimate sampling weights are random variables, dependent on the first phase of sampling. A new hybrid variance estimator, dependent on both model-based and design based ideas, is introduced. Theoretical and empirical justifications are given which demonstrate that the proposed method handles well the difficult aspects of this sample design.