2007/07/14 by Xinjia Chen, Chen, Xinjia · 1 citation
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning and Algorithms #Machine Learning and Data Classification #Methodology (stat.ME) #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.0707.2113
18 pages, no figures, removed typos
openalex publication_date 2007/07/14 · arxiv created 2007/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such a very old but also extremely important problem and demonstrate that the difficulty for obtaining the exact solution is not insurmountable. Unlike the classical approximate sample size method based on the central limit theorem, we develop a new approach for computing the minimum sample size that does not require any approximation. Moreover, our approach overcomes the conservatism of existing rigorous sample size methods derived from Bernoulli's theorem or Chernoff bounds. Our computational machinery consists of two essential ingredients. First, we prove that the minimum of coverage probability with respect to a binomial parameter bounded in an interval is attained at a discrete set of finite many values of the binomial parameter. This allows for reducing infinite many evaluations of coverage probability to finite many evaluations. Second, a recursive bounding technique is developed to further improve the efficiency of computation.