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.
"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