Minimal Sufficiency in Rare Populations

作     者：Mohammad Moradi Jennifer A. Brown Miriam Hodge 

作者机构：Department of Science Razi University Kermanshah 67146 Iran Department of Mathematics and Statistics University of Canterbury Christchurch 8011 New Zealand 

出 版 物：《Journal of Mathematics and System Science》 (数学和系统科学（英文版）)

年 卷 期：2012年第2卷第5期

页      码：281-285页

摘      要：It is well understood that for conventional survey designs the set of unordered distinct units in a sample is a minimally sufficient statistic. This means that for inferential statistic of the sample, the value of the sampled units rather than the sample design is important. Sampling rare populations presents distinct challenges. Examples of rare populations are in biology with rare and endangered animals where there are only a few remaining individuals, or in social science, with the low incidence of people from an unusually high （or low） income group. Sampling rare populations tends to result in the case that many of the sample units do not contain information on the characteristic of interest （e.g., the rare animal, or people from the unusual income group）. For finite rare populations the set of unordered distinct rare-units in a sample is a minimally sufficient statistic. In an example case study of a rare buttercup, the properties of the minimal sufficient estimator are explored. We compare the efficiency of the estimator for the population total based on the minimally sufficient statistic, with the standard estimator for a range of sample sizes. The variance of the minimally sufficient estimator was always smaller than the variance of the sufficient estimator. For rare populations where non-rare units can be distinguished from rare units because they have the same fixed value, the minimal sufficient statistic is the rare units, if any, in the sample.

主 题 词：Rare population finite population sufficiency minimal sufficiency. 

学科分类：0710[理学-生物科学类] 02[经济学] 0202[经济学-财政学类] 020208[020208] 07[理学] 071007[071007] 0714[0714] 070103[070103] 0701[理学-数学类] 

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