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

AStA Advances in Statistical Analysis - Tập 96 Số 4 - Trang 451-465 - 2012
Ouassou, Idir1, Rachdi, Mustapha2
1Ecole Nationale des Sciences Appliquées, Université Cadi Ayyad, Marrakech, Maroc
2Laboratoire AGIM, FRE 3405 CNRS, TIMB Group, Université Pierre Mendès France (Grenoble 2), UFR SHS, Grenoble Cedex 09, France

Tóm tắt

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).

Tài liệu tham khảo

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