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

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

2009-11-08

arxiv.org/abs/0911.1497v4

Annals of Statistics 2011, Vol. 39, No. 4, 1852-1877

Mathematics

Statistics Theory

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

Scientific paper

10.1214/11-AOS888

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.

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