# Risk bounds for mixture density estimation

Alexander Rakhlin; Dmitry Panchenko; Sayan Mukherjee

ESAIM: Probability and Statistics (2005)

- Volume: 9, page 220-229
- ISSN: 1292-8100

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topRakhlin, Alexander, Panchenko, Dmitry, and Mukherjee, Sayan. "Risk bounds for mixture density estimation." ESAIM: Probability and Statistics 9 (2005): 220-229. <http://eudml.org/doc/246104>.

@article{Rakhlin2005,

abstract = {In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Estimator (MLE) and the greedy procedure described by Li and Barron (1999) under the additional assumption of boundedness of densities. We prove an $O(\frac\{1\}\{\sqrt\{n\}\})$ bound on the estimation error which does not depend on the number of densities in the estimated combination. Under the boundedness assumption, this improves the bound of Li and Barron by removing the $\log n$ factor and also generalizes it to the base classes with converging Dudley integral.},

author = {Rakhlin, Alexander, Panchenko, Dmitry, Mukherjee, Sayan},

journal = {ESAIM: Probability and Statistics},

keywords = {mixture density estimation; maximum likelihood; Rademacher processes; Mixture density estimation},

language = {eng},

pages = {220-229},

publisher = {EDP-Sciences},

title = {Risk bounds for mixture density estimation},

url = {http://eudml.org/doc/246104},

volume = {9},

year = {2005},

}

TY - JOUR

AU - Rakhlin, Alexander

AU - Panchenko, Dmitry

AU - Mukherjee, Sayan

TI - Risk bounds for mixture density estimation

JO - ESAIM: Probability and Statistics

PY - 2005

PB - EDP-Sciences

VL - 9

SP - 220

EP - 229

AB - In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Estimator (MLE) and the greedy procedure described by Li and Barron (1999) under the additional assumption of boundedness of densities. We prove an $O(\frac{1}{\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination. Under the boundedness assumption, this improves the bound of Li and Barron by removing the $\log n$ factor and also generalizes it to the base classes with converging Dudley integral.

LA - eng

KW - mixture density estimation; maximum likelihood; Rademacher processes; Mixture density estimation

UR - http://eudml.org/doc/246104

ER -

## References

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- [13] S.A. van de Geer, Empirical Processes in M-Estimation. Cambridge University Press (2000). Zbl1179.62073
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