Bounds for Bayesian order identification with application to mixtures

• 成果类型: Article
• 署名作者: Chambaz, Antoine; Rousseau, Judith
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000857
• 发表日期: 2008
• 页码: 938-962
• 关键词: CONVERGENCE-RATES

摘要

The efficiency of two Bayesian order estimators is studied. By using nonparametric techniques, we prove new underestimation and overestimation bounds. The results apply to various models, including mixture models. In this case, the errors are shown to be O(e(-an)) and O((log n)(b) / root n) (a, b > 0), respectively.