Local linear regression for functional data

Alain Berlinet (1) , Abdallah Elamine (1) , André Mas (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: Kernel; Regression model; Functional Data; Inverse problem; Small ball probability; Mean square error

Domaines: Statistiques [math.ST]

Alain Berlinet, Abdallah Elamine, André Mas. Local linear regression for functional data. Annals of the Institute of Statistical Mathematics, 2011, 63, pp.1047-1075. ⟨10.1007/s10463-010-0275-8⟩. ⟨hal-00182746⟩