Generalized maximum likelihood estimates for exponential families

• 成果类型: Article
• 署名作者: Csiszar, Imre; Matus, Frantisek
• 署名单位: Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0084-z
• 发表日期: 2008
• 页码: 213-246
• 关键词: closures

摘要

For a standard full exponential family on R-d, or its canonically convex subfamily, the generalized maximum likelihood estimator is an extension of the mapping that assigns to the mean a is an element of R-d of a sample for which a maximizer nu* of a corresponding likelihood function exists, the member of the family parameterized by nu*. This extension assigns to each a is an element of R-d with the likelihood function bounded above, a member of the closure of the family in variation distance. Its detailed description, complete characterization of domain and range, and additional results are presented, not imposing any regularity assumptions. In addition to basic convex analysis tools, the authors' prior results on convex cores of measures and closures of exponential families are used.