A comparison of some estimators of a set of population totals

The Population Estimates Program of Statistics Canada has traditionally been benchmarked to the most recent census, with no allowance for census coverage error. Because of a significant increase in the level of undercoverage in the 1986 Census, however, Statistics Canada is considering the possibility of adjusting the base population of the estimates program for net census undercoverage. This paper develops and compares four estimators of such a base population: the unadjusted census counts, the adjusted census counts, a preliminary test estimator, and a composite estimator. A generalization of previously-proposed risk functions, known as the Weighted Mean Square Error (WMSE), is used as the basis of comparison. The WMSE applies not only to population totals, but to functions of population totals such as population shares and growth rates between censuses. The use of the WMSE to develop and evaluate small-area estimators in the context of census adjustment is also described.