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.
Keywords: rate adaptive density estimation, gaussian mixture clustering, hellinger risk, non asymptotic model selection
@article{PS_2013__17__698_0,
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},
volume = {17},
doi = {10.1051/ps/2012018},
mrnumber = {3126158},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2012018/}
}
TY - JOUR AU - Maugis-Rabusseau, C. AU - Michel, B. TI - Adaptive density estimation for clustering with gaussian mixtures JO - ESAIM: Probability and Statistics PY - 2013 SP - 698 EP - 724 VL - 17 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2012018/ DO - 10.1051/ps/2012018 LA - en ID - PS_2013__17__698_0 ER -
%0 Journal Article %A Maugis-Rabusseau, C. %A Michel, B. %T Adaptive density estimation for clustering with gaussian mixtures %J ESAIM: Probability and Statistics %D 2013 %P 698-724 %V 17 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2012018/ %R 10.1051/ps/2012018 %G en %F PS_2013__17__698_0
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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