Adaptive density estimation of stationary β-mixing and τ-mixing processes

We propose an algorithm to estimate the common density s of a stationary process X ₁,..., _Xn. We suppose that the process is either β or τ-mixing. We provide a model selection procedure based on a generalization of Mallows' C _p and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i. i. d. framework.