QUASI-CONCAVE DENSITY ESTIMATION

• 成果类型: Article
• 署名作者: Koenker, Roger; Mizera, Ivan
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Alberta
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS814
• 发表日期: 2010
• 页码: 2998-3027
• 关键词: maximum-likelihood-estimation; probability density

摘要

Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the square-root of the density to be concave. A limiting form of these estimators constrains solutions to the class of quasi-concave densities.