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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.
@article{PS_2013__17__740_0,
author = {Rachdi, Nabil and Fort, Jean-Claude and Klein, Thierry},
title = {Risk bounds for new {M-estimation} problems},
journal = {ESAIM: Probability and Statistics},
pages = {740--766},
publisher = {EDP-Sciences},
volume = {17},
year = {2013},
doi = {10.1051/ps/2012025},
mrnumber = {3126160},
zbl = {1287.65008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2012025/}
}
TY - JOUR AU - Rachdi, Nabil AU - Fort, Jean-Claude AU - Klein, Thierry TI - Risk bounds for new M-estimation problems JO - ESAIM: Probability and Statistics PY - 2013 SP - 740 EP - 766 VL - 17 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2012025/ DO - 10.1051/ps/2012025 LA - en ID - PS_2013__17__740_0 ER -
%0 Journal Article %A Rachdi, Nabil %A Fort, Jean-Claude %A Klein, Thierry %T Risk bounds for new M-estimation problems %J ESAIM: Probability and Statistics %D 2013 %P 740-766 %V 17 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2012025/ %R 10.1051/ps/2012025 %G en %F PS_2013__17__740_0
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
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