Revisiting variance estimation when independent samples intersect

When a sample is obtained by intersecting two independent samples, the variance and the estimator of variance of the expanded estimator can be decomposed in two different ways according to the sample used in the conditional expectations. Even if both methods give the same result, we show that with one decomposition, it is generally more practical to compute the variance and with the other one, it is more convenient to estimate the variance. These differences in the decompositions are due to simplifications in joint inclusion probabilities and this sheds light on two particular cases: the reverse approach used in the nonresponse case and the estimation of variance in two-stage sampling designs.

, Annual Meeting of the Statistical Society of Canada, Winnipeg, Canada