The Annals of Statistics

Bounds for Bayesian order identification with application to mixtures

Antoine Chambaz and Judith Rousseau

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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.

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

First available in Project Euclid: 13 March 2008

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Zentralblatt MATH identifier

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

Mixture model selection nonparametric Bayesian inference order estimation rate of convergence


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.

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