Domains of study and poststratification

Sugden and Smith (2002. J. Statist. Plann. Inference 102, 25–38) investigated conditions under which exact linear unbiased estimators of linear estimands, and also exact quadratic unbiased estimators of quadratic estimands, could be constructed under the randomisation approach. In this paper the method is applied to domains of study and extended to poststratified estimators of finite population totals. The resulting estimators generalise some of those in Doss et al. (1979. J. Statist. Plann. Inference 3, 235–247). Some further properties of these estimators are explored.