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August 2011 Optimal model selection for density estimation of stationary data under various mixing conditions
Matthieu Lerasle
Ann. Statist. 39(4): 1852-1877 (August 2011). DOI: 10.1214/11-AOS888

Abstract

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are β or τ-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1.

We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.

Citation

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Matthieu Lerasle. "Optimal model selection for density estimation of stationary data under various mixing conditions." Ann. Statist. 39 (4) 1852 - 1877, August 2011. https://doi.org/10.1214/11-AOS888

Information

Published: August 2011
First available in Project Euclid: 26 July 2011

zbMATH: 1227.62018
MathSciNet: MR2893855
Digital Object Identifier: 10.1214/11-AOS888

Subjects:
Primary: 62G07, 62G09
Secondary: 62M99

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • August 2011
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