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Adaptive density estimation for clustering with gaussian mixtures
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 698-724 Cet article a éte moissonné depuis la source Numdam

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Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum likelihood estimator is proposed for automatically selecting the number of mixture components. In the present paper, a collection of univariate densities whose logarithm is locally β-Hölder with moment and tail conditions are considered. We show that this penalized estimator is minimax adaptive to the β regularity of such densities in the Hellinger sense.

DOI : 10.1051/ps/2012018
Classification : 62G07, 62G20
Keywords: rate adaptive density estimation, gaussian mixture clustering, hellinger risk, non asymptotic model selection 
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     author = {Maugis-Rabusseau, C. and Michel, B.},
     title = {Adaptive density estimation for clustering with gaussian mixtures},
     journal = {ESAIM: Probability and Statistics},
     pages = {698--724},
     year = {2013},
     publisher = {EDP-Sciences},
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     doi = {10.1051/ps/2012018},
     mrnumber = {3126158},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2012018/}
}
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Maugis-Rabusseau, C.; Michel, B. Adaptive density estimation for clustering with gaussian mixtures. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 698-724. doi: 10.1051/ps/2012018

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