Bounds for Bayesian order identification with application to mixtures

Mathematics – Statistics Theory

Scientific paper

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Published in at http://dx.doi.org/10.1214/009053607000000857 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000857

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.

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