The Annals of Statistics

Bounds for Bayesian order identification with application to mixtures

Antoine Chambaz and Judith Rousseau

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Abstract

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(ean) and $O((\log n)^{b}/\sqrt{n})$ (a, b>0), respectively.

Article information

Source
Ann. Statist. Volume 36, Number 2 (2008), 938-962.

Dates
First available in Project Euclid: 13 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1205420524

Digital Object Identifier
doi:10.1214/009053607000000857

Mathematical Reviews number (MathSciNet)
MR2396820

Zentralblatt MATH identifier
1246.62083

Subjects
Primary: 62F05: Asymptotic properties of tests 62F12: Asymptotic properties of estimators 62G05: Estimation 62G10: Hypothesis testing

Keywords
Mixture model selection nonparametric Bayesian inference order estimation rate of convergence

Citation

Chambaz, Antoine; Rousseau, Judith. Bounds for Bayesian order identification with application to mixtures. Ann. Statist. 36 (2008), no. 2, 938--962. doi:10.1214/009053607000000857. https://projecteuclid.org/euclid.aos/1205420524


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