Volume 17, 2013
|Page(s)||740 - 766|
|Published online||04 November 2013|
Risk bounds for new M-estimation problems∗
1 EADS Innovation Works, 12 rue Pasteur, 92152 Suresnes, France
2 Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France
3 Université Paris Descartes, SPC, MAP5, 45 rue des Saints-Pères, 75006 Paris, France
4 Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France
Revised: 14 August 2012
In this paper, we consider a new framework where two types of data are available: experimental data Y1,...,Yn supposed to be i.i.d from Y and outputs from a simulated reduced model. We develop a procedure for parameter estimation to characterize a feature of the phenomenon Y. We prove a risk bound qualifying the proposed procedure in terms of the number of experimental data n, reduced model complexity and computing budget m. The method we present is general enough to cover a wide range of applications. To illustrate our procedure we provide a numerical example.
Mathematics Subject Classification: 65C60 / 60F05 / 62F12 / 60G20 / 65J22
Key words: M-estimation / inverse problems / empirical processes / oracle inequalities / model selection
© EDP Sciences, SMAI, 2013
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