A jackknife variance estimator for self-weighted two-stage samples

Self-weighted two-stage sampling designs are popular in practice as they simplify field-work. It is common in practice to compute variance estimates only from the first sampling stage, neglecting the second stage. This omission may induce a bias in variance estimation; especially in situations where there is low variability between clusters or when sampling fractions are non-negligible. We propose a design-consistent jackknife variance estimator that takes account of all stages via deletion of clusters and observations within clusters. The proposed jackknife can be used for a wide class of point estimators. It does not need joint-inclusion probabilities and naturally includes finite population corrections. A simulation study shows that the proposed estimator can be more accurate than standard jackknifes (Rao, Wu, and Yue (1992)) for self-weighted two-stage sampling designs