HORVITZ-THOMPSON THEOREM AS A TOOL FOR GENERALIZATION OF PROBABILITY SAMPLING TECHNIQUES

Abstract

The Horvitz-Thompson estimator is often presented in the context of an estimator based on the concept of variable probability sampling. In truth, however, the Horvitz-Thompson theorem is arguably a lot more versatile than this narrow perspective. The main objective of this article is to review the application of the generalization provided by the Horvitz-Thompson theorem to basic sampling methodology, and to estimators of means and variances. It is further shown that the Horvitz-Thompson estimator also serves as the basis for a general strategy for consistent estimation.