Optimal model selection for stationary data under various mixing conditions

In this paper, we address the problem of model selection by minimization of a penalized criterion, for non necessary independent random variables. The penalty is obtained by a bloc-resampling estimator of the ideal penalty. We also propose to optimize the leading constant in this penalty, using the slope algorithm. When the data are $\beta$ or $\tau$-mixing, our estimators satisfy oracle inequalities with leading constant asymptotically equal to $1$ and we prove that the slope heuristic holds.