| Abstract: | We re-examine the criteria of “hyper-admissibility” and “necessary bestness”, for the choice of estimator, from the point of view of their relevance to the design of actual surveys. Both these criteria give rise to a unique choice of estimator (viz. the Horvitz-Thompson estimator ?HT) whatever be the character under investigation or sample design. However, we show here that the “principal hyper-surfaces” (or “domains”) of dimension one (which are practically uninteresting)play the key role in arriving at the unique choice. A variance estimator v1(?HT) (due to Horvitz-Thompson), which takes negative values “often”, is shown to be uniquely “hyperadmissible” in a wide class of unbiased estimators of the variance of ?HT. Extensive empirical evidence on the superiority of the Sen-Yates-Grundy variance estimator v2(?HT) over v1(?HT) is presented. |
