Replication variance estimation in unequal probability sampling without replacement: One‐stage and two‐stage

Abstract

AbstractReplication‐based variance estimation methods including the bootstrap, balanced repeated replication, and the Jackknife have been studied extensively. They have been applicable primarily to stratified multistage sampling designs in which the clusters within strata are sampled with replacement or the first‐stage sampling fraction is negligible with a notable exception of a two‐stage cluster sampling with equal probability and without replacement in Rao & Wu (1988). It is common practice, however, that the first‐stage sampling fraction may not be negligible, resulting in overestimation. To alleviate this practical issue, we derive the balanced repeated replication methods and the bootstrap methods for one‐ and two‐stage stratified unequal probability sampling, where the sampling fractions are not negligible. The asymptotic property of the proposed methods is studied. In addition, the methodologies are applied to a simulated population with characteristics of a real sample survey. The Canadian Journal of Statistics 41: 696‐716; 2013 © 2013 Statistical Society of Canada