A0481
Title: Minimax estimation in the functional regression model with a functional output
Authors: Gaelle Chagny - CNRS, Universite de Rouen Normandie (France) [presenting]
Anouar Meynaoui - IRMAR Universite Rennes 2 (France)
Angelina Roche - Universite Paris Dauphine (France)
Abstract: The problem of nonparametric estimation of a linear regression model is addressed, where both the covariate and the response variable are functional random variables. Projection estimators for the conditional expectation operator are introduced. Their prediction risk achieves a non-asymptotic sharp upper-bound as a classical bias-variance compromise. Then, the automatic trade-off is realized thanks to a model selection device (penalized criterion). An oracle-type inequality is proved, and convergence rates are derived from ellipsoidal regularity spaces. They match with a lower-bound (also proved), and thus, the procedure is optimal in the adaptive and in the minimax sense. A numerical study (over simulated data and over a real-data set) is also presented.
