OPTIMAL MODEL SELECTION FOR DENSITY ESTIMATION OF STATIONARY DATA UNDER VARIOUS MIXING CONDITIONS

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