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Risk bounds for new M-estimation problems

Published online by Cambridge University Press:  04 November 2013

Nabil Rachdi
Affiliation:
EADS Innovation Works, 12 rue Pasteur, 92152 Suresnes, France. [email protected] 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; [email protected]
Thierry Klein
Affiliation:
Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France; [email protected]
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2013

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