Regression operator estimation by delta-sequences method for functional data and its applications

In this paper, we introduce a somewhat more general class of nonparametric estimators (delta-sequences estimators) for estimating an unknown regression operator from noisy data. The regressor is assumed to take values in an infinite-dimensional separable Banach space, when the response variable is a scalar. Under some general conditions, we establish the uniform almost-complete convergence with the rates of these estimators. Moreover, we give some particular cases of our results, which can also be considered as novel in the finite-dimensional setting. Moreover, after giving some examples of the impact of our results, we show how to use them in some statistical applications (prediction procedure and curve discrimination). Copyright Springer-Verlag 2012