Oracle inequalities for new M-estimation and model selection problems

Nabil Rachdi (1, 2) , Jean-Claude Fort (3) , Thierry Klein (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 EADS Innovation Works [Toulouse]
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

In this paper, we develop new algorithms for parameter estimation and model selection in the case of models type Input/Output in order to represent and to characterize a phenomenon Y. From experimental data Y_{1},...,Y_{n} supposed to be i.i.d from Y, we prove oracle inequalities qualifying the proposed procedures in terms of the number of experimental data n, computing budget m and model complexity. The methods we present are general enough which should cover a wide range of applications.

Mots clés: M-estimation; Inverse problems; Empirical processes; Oracle inequalities; Model selection

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

Nabil Rachdi, Jean-Claude Fort, Thierry Klein. Oracle inequalities for new M-estimation and model selection problems. 2010. ⟨hal-00537236v1⟩