Exact Optimal Confidence Intervals for Hypergeometric Parameters

• 成果类型: Article
• 署名作者: Wang, Weizhen
• 署名单位: Beijing University of Technology; University System of Ohio; Wright State University Dayton
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.966191
• 发表日期: 2015
• 页码: 1491-1499
• 关键词: estimating animal abundance; binomial proportion; statistical-inference; APPROXIMATE; estimators; variance; BIAS

摘要

For a hypergeometric distribution, denoted by Hyper(M, N, n), where N is the population size, M is the number of population units with some attribute, and n is the given sample size, there are two parametric cases: (i) N is unknown and M is given; (ii) M is unknown and N is given. For each case, we first show that the minimum coverage probability of commonly used approximate intervals is much smaller than the nominal level for any n, then we provide exact smallest lower and upper one-sided confidence intervals and an exact admissible two-sided confidence interval, a complete set of solutions, for each parameter. Supplementary materials for this article are available online.