Fractal dimensionality and regression estimation in semi-normed vectorial spaces

This Note presents a nonparametric model for scalar response regression problems when the explanatory variable is valued in some semi-normed vectorial space. Nonparametric estimates are proposed and some asymptotic results are stated. It turns out that the rates of convergence are crucially linked with the fractal dimensionality of the underlying measure of probability of the explanatory variable. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.