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Bounds for Bayesian order identification with application to mixtures. (English) Zbl 1246.62083

Summary: 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.

MSC:

62G05 Nonparametric estimation
62F15 Bayesian inference
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