Multivariate wavelet estimators for weakly dependent processes: strong consistency rate

Abstract

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 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 -weak dependence, including mixing concepts and adapted to diverse classes of interesting statistical processes, essentially the general Bernoulli shifts and the Markov sequences.