Far East Journal of Theoretical Statistics
Volume 29, Issue 2, Pages 129 - 136
(November 2009)
|
|
ESTIMATING PROPORTIONS WITH UNEQUAL SAMPLING PROBABILITIES: THE BASU’S ELEPHANT PROBLEM REVISITED
Jose M. Pavía (Spain)
|
Abstract: When sampling a finite universe with unequal selection probabilities, the unbiased estimators recommended can yield inadmissible outcomes. Although Basu early warned about this weakness of the Horvitz-Thompson estimation method, the very unrealistic Basu’s example rapidly relaxed statisticians and this crucial detail was almost forgotten and systematically omitted in textbooks. In predicting proportions, however, this shortfall is more visible and can appear even with reasonable sampling plans. This paper shows it first using an unrealistic laboratory design and later through a real data application. After mentioning a feasible solution, this note proposes to open a debate and suggests return to survey-sampling and inference foundations on the search for a solution that can widely be accepted. |
Keywords and phrases: Horvitz-Thompson estimator, finite populations, multi-stage sampling, sampling with replacement, sampling without replacement, unequal probability sampling. |
|
Number of Downloads: 249 | Number of Views: 625 |
|