Functional linear regression with derivatives

André Mas (1) , Besnik Pumo (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 INHP - Institut National d'Horticulture et du Paysage

We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronized penalization. An asymptotic expansion of the mean square prevision error is given. The model and the method are applied to a benchmark dataset of spectrometric curves and compared with other functional models.

Mots clés: Linear regression model; Functional data; Differential operator; Spectrometric curves; Penalization

Domaines: Statistiques [math.ST]

André Mas, Besnik Pumo. Functional linear regression with derivatives. Journal of Nonparametric Statistics, 2009, 21 (1), pp.19-40. ⟨10.1080/10485250802401046⟩. ⟨hal-00104298⟩