Optimal model selection for density estimation of stationary data under various mixing conditions

Abstract

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are $\beta$ or $\tau$-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.

Published in at http://dx.doi.org/10.1214/11-AOS888 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Concentration around the mean for maxima of empirical processes
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• Model selection by resampling penalization
• V-fold cross-validation improved: V-fold penalization
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Cited by in corpus (4)

• Choice of V for V-Fold Cross-Validation in Least-Squares Density Estimation
• Minimal penalties and the slope heuristics: a survey
• Rejoinder on: Minimal penalties and the slope heuristics: a survey
• Adaptive directional estimator of the density in R^d for independent and mixing sequences