On the acceleration of some empirical means with application to nonparametric regression

Bernard Delyon, François Portier

Let $(X_1,\dots ,X_n)$ be an i.i.d. sequence of random variables in ${\mathbb{R}}^d$, $d\ge 1$, for some function $\phi :{\mathbb{R}}^d\mathring{\mathbb{R}}$, under regularity conditions, we show that \begin{align*} n^…