# 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

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topRachdi, 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 -

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