ALMOST SURE UNIQUENESS OF A GLOBAL MINIMUM WITHOUT CONVEXITY

• 成果类型: Article
• 署名作者: Cox, Gregory
• 署名单位: Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1829
• 发表日期: 2020
• 页码: 584-606
• 关键词: maximum-likelihood estimator; nonconcave penalized likelihood; mixture likelihoods; EXISTENCE; models; inference; geometry; weak

摘要

This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification.