Almost sure convergence of recursive kernel estimatiors of the density and the regression under η− weak dependence

Abstract

The result of this work addresses the consistency of recursive kernel estimates of the regression and density functions. We provide almost sure convergence under $\eta -$weak dependence using exponential inequality adapted to this context of dependence. Rates of convergence are derived also.

Keywords:

• Recursive kernel estimates
• density and regression
• almost sure convergence
• $\eta -$weak dependence
• rates of convergence

Acknowledgments

We are very grateful to the Associate Editor and to the referees for their valuable comments and suggestions.