Kernel regression estimation in a Banach space

In this paper, we study a nonparametric regression estimator when the response variable is in a separable Banach space and the explanatory variable takes values in a separable semi-metric space. Under general conditions, we establish some asymptotic results and give upper bounds for the pp-mean and almost sure (pointwise and integrated) estimation errors. Finally, we present the case where the explanatory variable is the Wiener process.