Search

Your search keyword '"Taupin , Marie-Luce"' showing total 8 results
Start Over Author "Taupin , Marie-Luce" Topic [math.math-st]mathematics [math]/statistics [math.st]
8 results on '"Taupin , Marie-Luce"'

1. RKHSMetaMod: An R package to estimate the Hoeffding decomposition of an unknown function by solving RKHS ridge group sparse optimization problem

Author

Kamari, Halaleh, Huet, Sylvie, Taupin, Marie-Luce, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)

Subjects
meta model, Reproducing Kernel Hilbert Spaces, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Computer Science::Mathematical Software, Hoeffding decomposition, optimization problem, Sobol indices
Abstract

In the context of the Gaussian regression model, the package RKHSMetaMod allows to estimate a meta model by solving the ridge group sparse optimization problem based on the Reproducing Kernel Hilbert Spaces (RKHS). The obtained estimator is an additive model that satisfies the properties of the Hoeffding decomposition, and its terms estimate the terms in the Hoeffding decomposition of the unknown regression function. The estimators of the Sobol indices are deduced from the estimated meta model. This package provides an interface from R statistical computing environment to the C++ libraries Eigen and GSL. In order to speed up the execution time, almost all of the functions of the RKHSMetaMod package are written using the efficient C++ libraries through RcppEigen and RcppGSL packages. These functions are then interfaced in the R environment in order to propose an user friendly package.

Published
2019

2. MODEL SELECTION IN LOGISTIC REGRESSION

Author

Kwemou, Marius, Taupin, Marie-Luce, Tocquet, Anne-Sophie, laboratoire d'Etudes et de recherches en Statistiques et Développement (LERSTAD), Université Gaston Bergé Sénégal, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), INRA - Mathématiques et Informatique Appliquées (Unité MIAJ), Institut National de la Recherche Agronomique (INRA), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
Statistics::Theory, model selection, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], logistic regression, Secondary 62G05, FOS: Mathematics, Statistics::Methodology, projection AMS 2000 MSC: Primary 62J02, Mathematics - Statistics Theory, Statistics Theory (math.ST), 62F12, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], 62G20
Abstract

This paper is devoted to model selection in logistic regression. We extend the model selection principle introduced by Birg\'e and Massart (2001) to logistic regression model. This selection is done by using penalized maximum likelihood criteria. We propose in this context a completely data-driven criteria based on the slope heuristics. We prove non asymptotic oracle inequalities for selected estimators. Theoretical results are illustrated through simulation studies.

Published
2015

3. Adaptive density deconvolution for dependent inputs with measurement errors

Author

Comte, Fabienne, Taupin, Marie-Luce, Dedecker, Jérôme, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Statistique Théorique et Appliquée ( LSTA ), Université Pierre et Marie Curie - Paris 6 ( UPMC ), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2008

4. New M-estimators in semiparametric regression with errors in variables

Author

Butucea, Cristina, Taupin, Marie-Luce, Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Modélisation aléatoire de Paris X ( MODAL'X ), Université Paris Nanterre ( UPN ), Laboratoire de Probabilités et Modèles Aléatoires ( LPMA ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)

Subjects
consistency, ordinary smooth and super-smooth functions, rates of convergence, semiparametric nonlinear regression, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], M-estimators, [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], deconvolution kernel estimator, 2000 MSC, Primary 62J02, 62F12, Secondary 62G05, 62G20, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], errors-in-variables model, Asymptotic normality, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]
Abstract

In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\varepsilon$ involving independent and unobserved random variables $X,\xi,\varepsilon$ plus a regression function $f_{\theta^0}$, known up to some finite dimensional $\theta^0$. The common densities of the $X_i$'s and of the $\xi_i$'s are unknown whereas the distribution of $\varepsilon$ is completely known. We aim at estimating the parameter $\theta^0$ by using the observations $(Y_1,Z_1),\cdots, (Y_n,Z_n)$. We propose two estimation procedures based on the least square criterion $\tilde S_{\theta^0,g}(\theta)=\mathbb{E}_{\theta^0,g}[((Y-f_\theta(X))^2w(X)]$ where $w$ is some weight function, to be chosen. In the first estimation procedure, $w$ does not depend on $\theta$ and the distribution of the $\xi$'s is unknown. The second estimation procedure is based on $S_{\theta^0,g}(\theta)=\mathbb{E}_{\theta^0,g}[((Y-f_\theta(X))^2-\sigma_{\xi,2}^2)w_\theta(X)]$ where $w_\theta$ is positive weight function, to be chosen, and requires the knowledge of $\sigma_{\xi,2}^2=\mbox{Var}(\xi)$. In both cases, we propose two estimators and derive upper bounds for the risk of those estimators, depending on the smoothness of the errors density $p_\varepsilon$ and on the smoothness properties of $w(x)f_\theta(x)$ or $w_\theta(x)f_\theta(x)$ with respect to $x$. Furthermore we give sufficient conditions that ensure that the parametric rate of convergence is achieved. We provide practical recipes for the choice of $w$ or $ w_\theta$ in the case of nonlinear regressionfunctions which are smooth on pieces allowing to gain in the order of the rate of convergence, up to the parametric rate in some cases.

Published
2008

5. Semi-parametric estimation of the hazard function in a model with covariate measurement error

Author

Martin-Magniette, Marie-Laure, Taupin, Marie-Luce, Mathématiques et Informatique Appliquées ( MIA-Paris ), Ecole Nationale du Génie Rural, des Eaux et des Forêts ( ENGREF ) -Institut National de la Recherche Agronomique ( INRA ) -Institut National Agronomique Paris-Grignon ( INA P-G ), Unité de recherche en génomique végétale ( URGV ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Mathématiques et Informatique Appliquées (MIA-Paris), Ecole Nationale du Génie Rural, des Eaux et des Forêts (ENGREF)-Institut National de la Recherche Agronomique (INRA)-Institut National Agronomique Paris-Grignon (INA P-G), Unité de recherche en génomique végétale (URGV), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), and Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Université Paris Descartes - Paris 5 (UPD5)

Subjects
62G05, 62F12, 62N01, 62N02, Cox model censoring, MSC Classifications (2000): Primary 62G05, 62F12,62N01, 62N02, Secondary 62J02, Mathematics - Statistics Theory, Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], nonparametric estimation, 62J02, [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], survival analysis, Semiparametric estimation, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], errors-in-variables model, FOS: Mathematics, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], excess risk model
Abstract

We consider a model where the failure hazard function, conditional on a covariate $Z$ is given by $R(t,\theta^0|Z)=\eta_{\gamma^0}(t)f_{\beta^0}(Z)$, with $\theta^0=(\beta^0,\gamma^0)^\top\in \mathbb{R}^{m+p}$. The baseline hazard function $\eta_{\gamma^0}$ and relative risk $f_{\beta^0}$ belong both to parametric families. The covariate $Z$ is measured through the error model $U=Z+\varepsilon$ where $\varepsilon$ is independent from $Z$, with known density $f_\varepsilon$. We observe a $n$-sample $(X_i, D_i, U_i)$, $i=1,\ldots,n$, where $X_i$ is the minimum between the failure time and the censoring time, and $D_i$ is the censoring indicator. We aim at estimating $\theta^0$ in presence of the unknown density $g$. Our estimation procedure based on least squares criterion provide two estimators. The first one minimizes an estimation of the least squares criterion where $g$ is estimated by density deconvolution. Its rate depends on the smoothnesses of $f_\varepsilon$ and $f_\beta(z)$ as a function of $z$,. We derive sufficient conditions that ensure the $\sqrt{n}$-consistency. The second estimator is constructed under conditions ensuring that the least squares criterion can be directly estimated with the parametric rate. These estimators, deeply studied through examples are in particular $\sqrt{n}$-consistent and asymptotically Gaussian in the Cox model and in the excess risk model, whatever is $f_\varepsilon$.

Published
2006

6. Nonparametric Estimation of the Regression Function in an Errors-in-Variables Model

Author

Comte , Fabienne, Taupin , Marie-Luce, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), and Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
Projection estimators, Mathematics - Statistics Theory, Nonparametric regression, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Statistics Theory (math.ST), [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], Errors-in-variables, Density deconvolution, (Secondary) 62G05, 62G20, MSC 2000 Primary 62G08, 62G07. Secondary 62G05, 62G20, Adaptive estimation, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Minimax estimation, (Primary) 62G08, 62G07, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]
Abstract

We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, \; Z=X+\sigma\varepsilon$, involving independent and unobserved random variables $X,\xi,\varepsilon$. The density $g$ of $X$ is unknown, whereas the density of $\sigma\varepsilon$ is completely known. Using the observations $(Y_i, Z_i)$, $i=1,\cdots,n$, we propose an estimator of the regression function $f$, built as the ratio of two penalized minimum contrast estimators of $\ell=fg$ and $g$, without any prior knowledge on their smoothness. We prove that its $\mathbb{L}_2$-risk on a compact set is bounded by the sum of the two $\mathbb{L}_2(\mathbb{R})$-risks of the estimators of $\ell$ and $g$, and give the rate of convergence of such estimators for various smoothness classes for $\ell$ and $g$, when the errors $\varepsilon$ are either ordinary smooth or super smooth. The resulting rate is optimal in a minimax sense in all cases where lower bounds are available.

Published
2005
Full Text
View/download PDF

7. Metamodel construction for sensitivity analysis

Author

Marie-Luce Taupin, Sylvie Huet, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Taupin, Marie-Luce, Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
T57-57.97, Statistics::Theory, Applied mathematics. Quantitative methods, Computer science, Gaussian, Hilbert space, Estimator, Mathematics - Statistics Theory, Regression analysis, Multivariate normal distribution, Statistics Theory (math.ST), Metamodeling, Statistics::Computation, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], QA1-939, symbols, FOS: Mathematics, Statistiques (Mathématiques), Sensitivity (control systems), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Algorithm, Mathematics, Reproducing kernel Hilbert space
Abstract

We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to a functional ANOVA decomposition. The estimation of the metamodel is carried out via a penalized least-squares minimization allowing to select the subsets of variables that contribute to predict the output. It allows to estimate the sensitivity indices of m. We establish an oracle-type inequality for the risk of the estimator, describe the procedure for estimating the metamodel and the sensitivity indices, and assess the performances of the procedure via a simulation study., Nous considérons l’estimation d’un méta-modèle d’un modèle complexe m à partir des observations d’un n-échantillon dans un modèle de régression gaussien. Nous en déduisons une estimation des indices de sensibilité de m. Notre approche combine les méthodes d’analyse de sensibilité de modèles complexes et les outils statistiques de l’estimation non-paramétrique en régression multivariée. Elle repose sur la construction d’un méta-modèle qui approche la décomposition de Hoeffding-Sobol de m. Ce méta-modèle appartient à un espace de Hilbert à noyau reproduisant qui est lui-même la somme directe d’espaces de Hilbert, permettant ainsi une décomposition de type ANOVA. On en déduit des estimateurs des indices de sensibilité de m. Nous établissons une inégalité de type oracle pour le risque de l’estimateur, nous décrivons la procédure pour estimer le méta-modèle et les indices de sensibilité, et évaluons les performances de notre méthode à l’aide d’une étude de simulations.

Published
2017
Full Text
View/download PDF

8. Estimation in autoregressive model with measurement error

Author

Marie-Luce Taupin, Adeline Samson, Jérôme Dedecker, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Université Paris Descartes - Paris 5 (UPD5), Laboratoire Statistique et Génome (SG), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Statistique et Génome ( SG ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -Centre National de la Recherche Scientifique ( CNRS ), Taupin, Marie-Luce, and Laboratoire de Mathématiques et Modélisation d'Evry (LaMME)

Subjects
Statistics and Probability, Statistics::Theory, Weight function, Mathematics - Statistics Theory, Statistics Theory (math.ST), deconvolution, semi-parametric model, 01 natural sciences, Combinatorics, 010104 statistics & probability, Mixing (mathematics), [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, mixing, [INFO]Computer Science [cs], [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], [MATH]Mathematics [math], 0101 mathematics, Mathematics, Observational error, Smoothness (probability theory), Primary 62J02, 62F12, Secondary 62G05, 62G20, 010102 general mathematics, Estimator, semi-parametric nonlinear autoregressive model, autoregressive model, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], Semiparametric model, Distribution (mathematics), Autoregressive model, weak dependent, markov chain, Markov chain
Abstract

International audience; Consider an autoregressive model with measurement error: we observe $Z_i=X_i+\varepsilon_i$, where $X_i$ is a stationary solution of the equation $X_i=f_{\theta^0}(X_{i-1})+\xi_i$. The regression function $f_{\theta^0}$ is known up to a finite dimensional parameter $\theta^0$. The distributions of $X_0$ and $\xi_1$ are unknown whereas the distribution of $\varepsilon_1$ is completely known. We want to estimate the parameter $\theta^0$ by using the observations $Z_0,\ldots,Z_n$. We propose an estimation procedure based on a modified least square criterion involving a weight function $w$, to be suitably chosen. We give upper bounds for the risk of the estimator, which depend on the smoothness of the errors density $f_\varepsilon$ and on the smoothness properties of $w f_\theta$.

Published
2014
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results