# Adaptive density estimation for clustering with gaussian mixtures

C. Maugis-Rabusseau; B. Michel

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 698-724
- ISSN: 1292-8100

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topMaugis-Rabusseau, C., and Michel, B.. "Adaptive density estimation for clustering with gaussian mixtures." ESAIM: Probability and Statistics 17 (2013): 698-724. <http://eudml.org/doc/273632>.

@article{Maugis2013,

abstract = {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.},

author = {Maugis-Rabusseau, C., Michel, B.},

journal = {ESAIM: Probability and Statistics},

keywords = {rate adaptive density estimation; gaussian mixture clustering; hellinger risk; non asymptotic model selection; Gaussian mixture clustering; Hellinger risk},

language = {eng},

pages = {698-724},

publisher = {EDP-Sciences},

title = {Adaptive density estimation for clustering with gaussian mixtures},

url = {http://eudml.org/doc/273632},

volume = {17},

year = {2013},

}

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

PB - EDP-Sciences

VL - 17

SP - 698

EP - 724

AB - 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.

LA - eng

KW - rate adaptive density estimation; gaussian mixture clustering; hellinger risk; non asymptotic model selection; Gaussian mixture clustering; Hellinger risk

UR - http://eudml.org/doc/273632

ER -

## References

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