Asymptotics of the discrete log-concave maximum likelihood estimator and related applications

• 成果类型: Article
• 署名作者: Balabdaoui, Fadoua; Jankowski, Hanna; Rufibach, Kaspar; Pavlides, Marios
• 署名单位: Universite PSL; Universite Paris-Dauphine; York University - Canada; University of Zurich; Queens University Belfast
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12011
• 发表日期: 2013
• 页码: 769-790
• 关键词: inference; density; probability

摘要

The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well-specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true log-concave probability mass function. Both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the R package logcondiscr. We illustrate our theoretical results by using recent data from the H1N1 pandemic in Ontario, Canada.