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1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Abstract : We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the asymptotic mean square error. Computations involve a linear inverse problem as well as a representation of the small ball probability of the data and are based on recent advances in this area. The rate of convergence of our estimate outperforms those already obtained in the literature on this model.

keyword : Functional Data Regression model Kernel Mean square error Small ball probability Inverse problem

Author: Alain Berlinet - Abdallah Elamine - André Mas -

Source: https://hal.archives-ouvertes.fr/


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