Risk bounds for new M-estimation problems

Rachdi, Nabil; Fort, Jean‐Claude; Klein, Thierry

doi:10.1051/ps/2012025

Cited by 2 publications

(11 citation statements)

References 21 publications

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“…Under mild conditions, Theorem 3.1 in [21] proves the consistency in a general case when considering other contrast functions than log, and Theorem 6.2 in [20] shows the consistency in the special case of the log-contrast function. In such estimation procedure, we need a lot of system runs providing the desired observable h which can be CPU time expensive.…”

Section: Estimation Methodsmentioning

confidence: 96%

“…The method we present is taken from N. Rachdi et al [21]. The principle consists in estimating a parameter θ ∈ Θ ⊂ R k which minimizes "a distance" between the empirical distribution of the Y i 's (measurements) and the simulated distribution of the random variable h(X, θ) based on a sample h(X 1 , θ), ..., h(X m , θ) provided from numerical simulations, where X 1 , ..., X m are m simulations of the random variable X ∈ (X , P X ).…”

Section: Estimation Methodsmentioning

confidence: 99%

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Statistical inference for partial differential equations

et al. 2014

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Abstract. Many physical phenomena are modeled by parametrized PDEs. The poor knowledge on the involved parameters is often one of the numerous sources of uncertainties on these models. Some of these parameters can be estimated, with the use of real world data. The aim of this mini-symposium is to introduce some of the various tools from both statistical and numerical communities to deal with this issue. Parametric and non-parametric approaches are developed in this paper. Some of the estimation procedures require many evaluations of the initial model. Some interpolation tools and some greedy algorithms for model reduction are therefore also presented, in order to reduce time needed for running the model.

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Section: Estimation Methodsmentioning

confidence: 96%

Section: Estimation Methodsmentioning

confidence: 99%

Statistical inference for partial differential equations

et al. 2014

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“…Variable F , supposed to be independent of V , is a beta random variable on the interval [ min F , max F ] with shape parameters (7,2) where…”

Section: Noise Modelingmentioning

confidence: 99%

“…The purpose is now to estimate parameter θ ∈ Θ from the set of data M * ,1 f uel , ..., M * ,n f uel . In the next section, we propose an estimation procedure taken from [7].…”

Section: Noise Modelingmentioning

confidence: 99%

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Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model

Rachdi¹,

Fort²,

Klein³

2012

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial aircraft, where we only consider the Cruise phase. From a data base of fuel mass consumptions during the cruise phase, we aim at identifying the Specic Fuel Consumption (SF C) in a robust way, given the uncertainty of the cruise speed V and the lift-to-drag ratio F. In this paper, we present an estimation procedure based on Maximum-Likelihood estimation, taking into account this uncertainty. Résumé. Le problème inverse est une pratique assez courante en ingénierie, où le but est de déterminer les causes d'un certain phénomène à partir d'observations de ce dernier. Le phénomène mis en jeu est représenté par un modèle numérique, dont certaines composantes peuvent comporter une part de variabilité (voir [4]). Le phénomène étudié est la masse de fuel nécessaire pour eectuer une liaison xée avec un avion commercial, en ne considérant que la phase de Croisière. Le but étant, à partir de données de masses de fuel consommées en croisière, d'identier de manière robuste la consommation spécique SF C de la motorisation en tenant compte de l'incertitude sur la vitesse de croisière V et sur la nesse F de l'avion. Dans cet article, nous proposons une procédure d'estimation basée sur une méthode de maximum de vraisemblance, prenant en compte cette incertitude.

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Risk bounds for new M-estimation problems

Cited by 2 publications

References 21 publications

Statistical inference for partial differential equations

Statistical inference for partial differential equations

Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model

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