Multivariate wavelet estimators for weakly dependent processes: strong consistency rate

The present article focuses on the non parametric estimation of multivariate density and regression functions. We consider the non parametric linear wavelet-based estimators and investigate the strong consistency from the theoretical viewpoint. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of R-d, with the determination of the corresponding rates of convergence. As a main contribution, we relax some standard dependence conditions by considering the general concept of the causal (alpha) over tilde -weak dependence, including mixing concepts and adapted to diverse classes of interesting statistical processes, essentially the general Bernoulli shifts and the Markov sequences.