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Nonasymptotic Bounds for Bayesian Order Identification with Application to Mixtures

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  • Antoine Chambaz

    (Crest)

  • Judith Rousseau

    (Crest)

Abstract

The efficiency of two Bayesian order estimators is studied underweak assumptions. By using nonparametric techniques, we prove newnonasymptotic underestimation and overestimation bounds. The boundscompare favorably with optimal bounds yielded by the Stein lemmaand also with other known asymptotic bounds. The results applyto mixture models. In this case, the underestimation probabilitiesare bounded by a constant times e-an (some a > 0, all sample sizen = 1). The overestimation probabilities are bounded by 1/pn (alln larger than a known integer), up to a log n factor.

Suggested Citation

  • Antoine Chambaz & Judith Rousseau, 2005. "Nonasymptotic Bounds for Bayesian Order Identification with Application to Mixtures," Working Papers 2005-27, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-27
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    References listed on IDEAS

    as
    1. Guyon, Xavier & Yao, Jian-feng, 1999. "On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 221-249, August.
    2. Ishwaran H. & James L.F. & Sun J., 2001. "Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1316-1332, December.
    3. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
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