Variance approximation under balanced sampling

Jean-Claude Deville & Yves Tillé

Résumé A balanced sampling design has the interesting property that Horvitz-Thompson estimators of totals for a set of balancing variables are equal to the totals we want to estimate, therefore the variance of Horvitz-Thompson estimators of variables of interest are reduced in function of their correlations with the balancing variables. Since it is hard to derive an analytic expression for the joint inclusion probabilities, we derive a general approximation of variance based on a residual technique. This approximation is useful even in the particular case of unequal probability sampling with fixed sample size. Finally, a set of numerical studies with an original methodology allows to validate this approximation.
Citation Deville, J. C., & Tillé, Y. (2005). Variance approximation under balanced sampling. Journal of Statistical Planning and Inference, 128(2), 569-591.
Type Article de périodique (Anglais)
Date de publication 24-3-2005
Nom du périodique Journal of Statistical Planning and Inference
Volume 128
Numéro 2
Pages 569-591
URL http://www.sciencedirect.com/science/article/pii/S0378375...