Weighted finite population sampling to maximize entropy
| Autor: | Xiang-Hui Chen, Arthur P. Dempster, Jun Liu |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Statistics and Probability
Sample rotation education.field_of_study Applied Mathematics General Mathematics Population Estimator Agricultural and Biological Sciences (miscellaneous) Population sampling Combinatorics Sample size determination Entropy (information theory) Applied mathematics Uniqueness Statistics Probability and Uncertainty General Agricultural and Biological Sciences education Mathematics |
| Zdroj: | Biometrika. 81:457-469 |
| ISSN: | 1464-3510 0006-3444 |
| DOI: | 10.1093/biomet/81.3.457 |
| Popis: | SUMMARY Attention is drawn to a method of sampling a finite population of N units with unequal probabilities and without replacement. The method was originally proposed by Stern & Cover (1989) as a model for lotteries. The method can be characterized as maximizing entropy given coverage probabilities 7Ci, or equivalently as having the probability of a selected sample proportional to the product of a set of 'weights' wi. We show the essential uniqueness of the wi given the 7i, and describe practical, geometrically convergent algorithms for computing the wi from the 7i. We present two methods for stepwise selection of sampling units, and corresponding schemes for removal of units that can be used in connection with sample rotation. Inclusion probabilities of any order can be written explicitly in closed form. Second-order inclusion probabilities 7rij satisfy the condition 0< ij < 7ic 7j, which guarantees Yates & Grundy's variance estimator to be unbiased, definable for all samples and always nonnegative for any sample size. |
| Databáze: | OpenAIRE |
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