Convergence presque sûre de l'estimateur à noyau d'une fonction de régression additive sous une hypothèse de mélange

Abstract

We consider the multivariate regression function defined by m(·) = E(Y ∥X = ·), X ε R d . We propose to show that under the nonparametric additive regression model and under conditions of absolute regularity, the kernel integration method insures to obtain the optimal almost sure rate of convergence for univariate regression function.