Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : The efficiency of two Bayesian order estimators is studied under weak assumptions. By using nonparametric techniques, we prove new nonasymptotic underestimation and overestimation bounds. The bounds compare favorably with optimal bounds yielded by the Stein lemma and also with other known asymptotic bounds. The results apply to mixture models. In this case, the underestimation probabilities are bounded by a constant times $e^{-an}$ (some $a > 0$, all sample size $n geq 1$). The overestimation probabilities are bounded by $1/sqrt{n}$ (all $n$ larger than a known integer), up to a $log n$ factor.
Nonasymptotic bounds for Bayesian order identification with application to mixtures
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