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

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Lerasle, Matthieu
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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.
Comment: 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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Mathematics - Statistics Theory
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