Alternative utilizations of Information Criteria for Gaussian regression on a random design.

Guilhem Coq (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]

We consider the problem of estimating an unknown function f. Our data consist in a set of points in the plane, the abscisses of which are distributed according to a known density while their ordinates are the image of those abscisses by f deteriorated by a Gaussian white noise. To this end, we use general Information Criteria, also called penalized likelihood criteria. We introduce several methods of use of those criteria that present the advantage to have reasonnable computational complexity. We also show that those methods are as efficient as classical ones since they satisfy good asymptotic properties as well as an oracle inequality.

Mots clés: Information Criteria; model selection; Gaussian regression; oracle inequality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Guilhem Coq. Alternative utilizations of Information Criteria for Gaussian regression on a random design.. 2008. ⟨hal-00367551v1⟩