Risk bounds for new M-estimation problems
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 740-766.

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.

DOI : 10.1051/ps/2012025
Classification : 65C60, 60F05, 62F12, 60G20, 65J22
Mots-clés : M-estimation, inverse problems, empirical processes, oracle inequalities, model selection 
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Rachdi, Nabil; Fort, Jean-Claude; Klein, Thierry. Risk bounds for new M-estimation problems. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 740-766. doi : 10.1051/ps/2012025. http://www.numdam.org/articles/10.1051/ps/2012025/

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