A new replicate variance estimator for unequal probability sampling without replacement

Abstract

AbstractWe propose a new replicate variance estimator suitable for differentiable functions of estimated totals. The proposed variance estimator is defined for any unequal‐probability without‐replacement sampling design, it naturally includes finite population corrections and it allows two‐stage sampling. We show its design‐consistency and its close relationship with linearization variance estimators. When estimating a total, the proposed estimator reduces to the Horvitz–Thompson variance estimator. Simulations suggest that the proposed variance estimator is more stable than its replicate competitors. The Canadian Journal of Statistics 41: 508–524; 2013 © 2013 Statistical Society of Canada