LJKProbability & Statistics Seminar

On Thursday December 3 2009 at 14h00 in Salle 1  Tour IRMA

Seminary of Jérémie BIGOT (Université Paul Sabatier, Toulouse)

Nonlinear estimation in functional regression

Summary

This talk is concerned with the nonparametric estimation of a function f from a functional linear
regression model. We treat this problem as a linear illposed inverse problem in which the operator of the problem is stochastic. We consider three type of estimation methods:
 a linear one based on principal components decomposition of the stochastic operator
 non linear estimation by thresholding of empirical coeﬃcients together with Galerkin porjection methods on a linear space
 non linear estimation LASSO type procedure
A theoretical comparison of these three methods is presented using new oracle inequalities in that setting.
The ﬁnite sample performances of such estimates are also compared via some simulations.
This is a joint work with Sebastien Van Bellegem (Toulouse School of Economics, Université Toulouse 1).
