On the Admissibility of Proportions Observed in Samples Drawn with Replacement.
YALE UNIV NEW HAVEN CONN DEPT OF STATISTICS
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In sampling a finite unlabeled dichotomous population with replacement, the observed proportion as an estimator of the population proportion is admissible under squared-error loss when the sampling fraction is small, but is inadmissible when the fraction is large. Within an appropriately modified class of linear estimators, however, the observed proportion is always admissible for sampling fractions less than one. When the sampling fraction is greater than one, there is an obvious risk-reducing modification of the observed proportion the modified estimator is nonetheless inadmissible. Regardless of the sampling fraction, all admissible estimators for the unknown population proportion must belong to one of four disjoint and easily characterized families.
- Statistics and Probability