A quantitative Heppes theorem and multivariate Bernoulli distributions

• 成果类型: Article
• 署名作者: Fraiman, Ricardo; Moreno, Leonardo; Ransford, Thomas
• 署名单位: Universidad de la Republica, Uruguay; Universidad de la Republica, Uruguay; Laval University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad003
• 发表日期: 2023
• 页码: 293-314
• 关键词: probability-inequalities

摘要

Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in advance (as for instance for multivariate Bernoulli distributions), a single suitably chosen projection determines the distribution. Several applications of these results are considered.