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Risk bounds for new M-estimation problems∗

Published online by Cambridge University Press:  04 November 2013

Nabil Rachdi ,
Jean-Claude Fort  and
Thierry Klein
Nabil Rachdi
Affiliation:
EADS Innovation Works, 12 rue Pasteur, 92152 Suresnes, France. nabil.rachdi@eads.net Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France
Jean-Claude Fort
Affiliation:
Université Paris Descartes, SPC, MAP5, 45 rue des Saints-Pères, 75006 Paris, France; jean-claude.fort@parisdescartes.fr
Thierry Klein
Affiliation:
Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France; thierry.klein@math.univ-toulouse.fr

Abstract

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In this paper, we consider a new framework where two types of data are available:experimental dataY1,...,Ynsupposed 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 thephenomenon Y. We prove a risk bound qualifying the proposed procedure interms of the number of experimental data n, reduced model complexity andcomputing budget m. The method we present is general enough to cover awide range of applications. To illustrate our procedure we provide a numericalexample.

Keywords

M-estimationinverse problemsempirical processesoracle inequalitiesmodel selection

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 740 - 766
Copyright
© EDP Sciences, SMAI, 2013

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