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

##### Authors
Lerasle, Matthieu
##### Description
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)
##### Keywords
Mathematics - Statistics Theory