Large deviation results for the nonparametric regression function estimator on functional data

This paper is devoted to the study of large deviation behavior in the setting of the estimation of the regression function on functional data. A large deviation principle is stated for a process Z _n , defined below, allowing to derive a pointwise large deviation principle for the Nadaraya- Watson-type l-indexed regression function estimator as a by-product. Moreover, a uniform over VC-classes Chernoff type large deviation result is stated for the deviation of the l-indexed regression estimator.