Risk bounds for new M-estimation problems

Nabil Rachdi; Jean-Claude Fort; Thierry Klein

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 740-766
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Rachdi, Nabil, Fort, Jean-Claude, and Klein, Thierry. "Risk bounds for new M-estimation problems." ESAIM: Probability and Statistics 17 (2013): 740-766. <http://eudml.org/doc/273634>.

@article{Rachdi2013,
abstract = {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.},
author = {Rachdi, Nabil, Fort, Jean-Claude, Klein, Thierry},
journal = {ESAIM: Probability and Statistics},
keywords = {M-estimation; inverse problems; empirical processes; oracle inequalities; model selection; parameter estimation; numerical example},
language = {eng},
pages = {740-766},
publisher = {EDP-Sciences},
title = {Risk bounds for new M-estimation problems},
url = {http://eudml.org/doc/273634},
volume = {17},
year = {2013},
}

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
PB - EDP-Sciences
VL - 17
SP - 740
EP - 766
AB - 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.
LA - eng
KW - M-estimation; inverse problems; empirical processes; oracle inequalities; model selection; parameter estimation; numerical example
UR - http://eudml.org/doc/273634
ER -

References

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