A new replicate variance estimator for unequal probability sampling without replacement

We 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 (c) 2013 Statistical Society of Canada