Abstract—This paper establishes exponential inequalities for the probability of the distance between kernel estimator and its means in nonparametric regression problem with mixing variables. We consider an operator equation taking the following form Y=Aθ(Z)+ε, where A is a compact operator.
The goal is to estimate the functional θ when the variable Z is contaminated by measurements errors.

Index Terms—Convolution linear compact operator, kernel estimator, mixing process, non parametric regression.

The author is with Department of Mathematics, Univ. A/Mira Bejaia, Algeria (email: k_tim2002@yahoo.fr).

Cite: K. Belaide, "Exponential Inequalities in Functional Nonparametrics Regression for Mixing Process," International Journal of Applied Physics and Mathematics vol. 7, no. 4, pp. 251-258, 2017.