Abstract
This paper is devoted to the study of large deviation behaviors in the setting of the estimation of the regression function on functional data. A large deviation principle is stated for a process Zn, 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 Cherno? type large deviation result is stated for the deviation of the l-indexed regression estimator.
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