Bounds for Bayesian order identification with application to mixtures
Antoine Chambaz, Judith Rousseau
The Annals of Statistics · 2008 · Volume 36 · Issue 2
DOI: 10.1214/009053607000000857
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(e−an) and $O((\log n)^{b}/\sqrt{n})$ (a, b>0), respectively.
Keywords
62F05, 62F12, 62G05, 62G10, mixture, Model selection, nonparametric Bayesian inference, order estimation, rate of convergence
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