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. 





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