We consider density pointwise estimation in the i.i.d. case and look for bewst attainable asumptotic rates of convergence. The problem is adaptive, which means that the regularity parameter, b, describing the class of densities, varies in a set B.

We derive sharp asymptotic minimax bounds (that is, bounds which concern the exact asymptotic constant of the risk) for nonparametric density estimation based on weakly dependent observations. We study two particular problems for which there already exist such results in the case of independent...