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J.-M. Loubes
Institut de Mathématiques de Toulouse, Université de Toulouse, 31400 Toulouse, France

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Journal article
Published: 12 May 2021 in Viruses
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The spread of SARS-CoV-2 and the resulting disease COVID-19 has killed over 2.6 million people as of 18 March 2021. We have used a modified susceptible, infected, recovered (SIR) epidemiological model to predict how the spread of the virus in regions of France will vary depending on the proportions of variants and on the public health strategies adopted, including anti-COVID-19 vaccination. The proportion of SARS-CoV-2 variant B.1.1.7, which was not detected in early January, increased to become 60% of the forms of SARS-CoV-2 circulating in the Toulouse urban area at the beginning of February 2021, but there was no increase in positive nucleic acid tests. Our prediction model indicates that maintaining public health measures and accelerating vaccination are efficient strategies for the sustained control of SARS-CoV-2.

ACS Style

Chloé Dimeglio; Marine Milhes; Jean-Michel Loubes; Noémie Ranger; Jean-Michel Mansuy; Pauline Trémeaux; Nicolas Jeanne; Justine Latour; Florence Nicot; Cécile Donnadieu; Jacques Izopet. Influence of SARS-CoV-2 Variant B.1.1.7, Vaccination, and Public Health Measures on the Spread of SARS-CoV-2. Viruses 2021, 13, 898 .

AMA Style

Chloé Dimeglio, Marine Milhes, Jean-Michel Loubes, Noémie Ranger, Jean-Michel Mansuy, Pauline Trémeaux, Nicolas Jeanne, Justine Latour, Florence Nicot, Cécile Donnadieu, Jacques Izopet. Influence of SARS-CoV-2 Variant B.1.1.7, Vaccination, and Public Health Measures on the Spread of SARS-CoV-2. Viruses. 2021; 13 (5):898.

Chicago/Turabian Style

Chloé Dimeglio; Marine Milhes; Jean-Michel Loubes; Noémie Ranger; Jean-Michel Mansuy; Pauline Trémeaux; Nicolas Jeanne; Justine Latour; Florence Nicot; Cécile Donnadieu; Jacques Izopet. 2021. "Influence of SARS-CoV-2 Variant B.1.1.7, Vaccination, and Public Health Measures on the Spread of SARS-CoV-2." Viruses 13, no. 5: 898.

Journal article
Published: 22 February 2021 in Algorithms
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In this paper, we present a new framework dedicated to the robust detection of representative variables in high dimensional spaces with a potentially limited number of observations. Representative variables are selected by using an original regularization strategy: they are the center of specific variable clusters, denoted CORE-clusters, which respect fully interpretable constraints. Each CORE-cluster indeed contains more than a predefined amount of variables and each pair of its variables has a coherent behavior in the observed data. The key advantage of our regularization strategy is therefore that it only requires to tune two intuitive parameters: the minimal dimension of the CORE-clusters and the minimum level of similarity which gathers their variables. Interpreting the role played by a selected representative variable is additionally obvious as it has a similar observed behaviour as a controlled number of other variables. After introducing and justifying this variable selection formalism, we propose two algorithmic strategies to detect the CORE-clusters, one of them scaling particularly well to high-dimensional data. Results obtained on synthetic as well as real data are finally presented.

ACS Style

Camille Champion; Anne-Claire Brunet; Rémy Burcelin; Jean-Michel Loubes; Laurent Risser. Detection of Representative Variables in Complex Systems with Interpretable Rules Using Core-Clusters. Algorithms 2021, 14, 66 .

AMA Style

Camille Champion, Anne-Claire Brunet, Rémy Burcelin, Jean-Michel Loubes, Laurent Risser. Detection of Representative Variables in Complex Systems with Interpretable Rules Using Core-Clusters. Algorithms. 2021; 14 (2):66.

Chicago/Turabian Style

Camille Champion; Anne-Claire Brunet; Rémy Burcelin; Jean-Michel Loubes; Laurent Risser. 2021. "Detection of Representative Variables in Complex Systems with Interpretable Rules Using Core-Clusters." Algorithms 14, no. 2: 66.

Methodology article
Published: 27 October 2020 in BMC Bioinformatics
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Background Data obtained from flow cytometry present pronounced variability due to biological and technical reasons. Biological variability is a well-known phenomenon produced by measurements on different individuals, with different characteristics such as illness, age, sex, etc. The use of different settings for measurement, the variation of the conditions during experiments and the different types of flow cytometers are some of the technical causes of variability. This mixture of sources of variability makes the use of supervised machine learning for identification of cell populations difficult. The present work is conceived as a combination of strategies to facilitate the task of supervised gating. Results We propose optimalFlowTemplates, based on a similarity distance and Wasserstein barycenters, which clusters cytometries and produces prototype cytometries for the different groups. We show that supervised learning, restricted to the new groups, performs better than the same techniques applied to the whole collection. We also present optimalFlowClassification, which uses a database of gated cytometries and optimalFlowTemplates to assign cell types to a new cytometry. We show that this procedure can outperform state of the art techniques in the proposed datasets. Our code is freely available as optimalFlow, a Bioconductor R package at https://bioconductor.org/packages/optimalFlow. Conclusions optimalFlowTemplates + optimalFlowClassification addresses the problem of using supervised learning while accounting for biological and technical variability. Our methodology provides a robust automated gating workflow that handles the intrinsic variability of flow cytometry data well. Our main innovation is the methodology itself and the optimal transport techniques that we apply to flow cytometry analysis.

ACS Style

Eustasio Del Barrio; Hristo Inouzhe; Jean-Michel Loubes; Carlos Matrán; Agustín Mayo-Íscar. optimalFlow: optimal transport approach to flow cytometry gating and population matching. BMC Bioinformatics 2020, 21, 1 -25.

AMA Style

Eustasio Del Barrio, Hristo Inouzhe, Jean-Michel Loubes, Carlos Matrán, Agustín Mayo-Íscar. optimalFlow: optimal transport approach to flow cytometry gating and population matching. BMC Bioinformatics. 2020; 21 (1):1-25.

Chicago/Turabian Style

Eustasio Del Barrio; Hristo Inouzhe; Jean-Michel Loubes; Carlos Matrán; Agustín Mayo-Íscar. 2020. "optimalFlow: optimal transport approach to flow cytometry gating and population matching." BMC Bioinformatics 21, no. 1: 1-25.

Journal article
Published: 19 October 2018 in Journal of Multivariate Analysis
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Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the estimation of the quantiles of the empirical process of Wasserstein’s variation using a bootstrap procedure. We then use these results for statistical inference on a distribution registration model for general deformation functions. The tests are based on the variance of the distributions with respect to their Wasserstein’s barycenters for which we prove central limit theorems, including bootstrap versions.

ACS Style

Eustasio del Barrio; Paula Gordaliza; Hélène Lescornel; Jean-Michel Loubes. Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions. Journal of Multivariate Analysis 2018, 169, 341 -362.

AMA Style

Eustasio del Barrio, Paula Gordaliza, Hélène Lescornel, Jean-Michel Loubes. Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions. Journal of Multivariate Analysis. 2018; 169 ():341-362.

Chicago/Turabian Style

Eustasio del Barrio; Paula Gordaliza; Hélène Lescornel; Jean-Michel Loubes. 2018. "Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions." Journal of Multivariate Analysis 169, no. : 341-362.

Preprint
Published: 18 October 2018
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In this paper, we present a new explainability formalism to make clear the impact of each variable on the predictions given by black-box decision rules. Our method consists in evaluating the decision rules on test samples generated in such a way that each variable is stressed incrementally while preserving the original distribution of the machine learning problem. We then propose a new computation-ally efficient algorithm to stress the variables, which only reweights the reference observations and predictions. This makes our methodology scalable to large datasets. Results obtained on standard machine learning datasets are presented and discussed.

ACS Style

Francois Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Laurent Risser. Entropic Variable Boosting for Explainability and Interpretability in Machine Learning. 2018, 1 .

AMA Style

Francois Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Laurent Risser. Entropic Variable Boosting for Explainability and Interpretability in Machine Learning. . 2018; ():1.

Chicago/Turabian Style

Francois Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Laurent Risser. 2018. "Entropic Variable Boosting for Explainability and Interpretability in Machine Learning." , no. : 1.

Preprint
Published: 18 July 2018
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ACS Style

Eustasio Del Barrio; Paula Gordaliza; Jean-Michel Loubes. A Central Limit Theorem for $L_p$ transportation cost with applications to Fairness Assessment in Machine Learning. 2018, 1 .

AMA Style

Eustasio Del Barrio, Paula Gordaliza, Jean-Michel Loubes. A Central Limit Theorem for $L_p$ transportation cost with applications to Fairness Assessment in Machine Learning. . 2018; ():1.

Chicago/Turabian Style

Eustasio Del Barrio; Paula Gordaliza; Jean-Michel Loubes. 2018. "A Central Limit Theorem for $L_p$ transportation cost with applications to Fairness Assessment in Machine Learning." , no. : 1.

Preprint
Published: 17 July 2018
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ACS Style

Philippe Besse; Eustasio Del Barrio; Paula Gordaliza; Jean-Michel Loubes. Confidence Intervals for Testing Disparate Impact in Fair Learning. 2018, 1 .

AMA Style

Philippe Besse, Eustasio Del Barrio, Paula Gordaliza, Jean-Michel Loubes. Confidence Intervals for Testing Disparate Impact in Fair Learning. . 2018; ():1.

Chicago/Turabian Style

Philippe Besse; Eustasio Del Barrio; Paula Gordaliza; Jean-Michel Loubes. 2018. "Confidence Intervals for Testing Disparate Impact in Fair Learning." , no. : 1.

Journal article
Published: 12 October 2017 in IEEE Transactions on Information Theory
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Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.

ACS Style

Francois Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Nil Venet. A Gaussian Process Regression Model for Distribution Inputs. IEEE Transactions on Information Theory 2017, 64, 6620 -6637.

AMA Style

Francois Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet. A Gaussian Process Regression Model for Distribution Inputs. IEEE Transactions on Information Theory. 2017; 64 (10):6620-6637.

Chicago/Turabian Style

Francois Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Nil Venet. 2017. "A Gaussian Process Regression Model for Distribution Inputs." IEEE Transactions on Information Theory 64, no. 10: 6620-6637.

Preprint
Published: 31 January 2017
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Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.

ACS Style

François Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Nil Venet. Gaussian Process Regression Model for Distribution Inputs. 2017, 1 .

AMA Style

François Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet. Gaussian Process Regression Model for Distribution Inputs. . 2017; ():1.

Chicago/Turabian Style

François Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Nil Venet. 2017. "Gaussian Process Regression Model for Distribution Inputs." , no. : 1.

Preprint
Published: 30 January 2017
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Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.

ACS Style

François Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Nil Venet. A Gaussian Process Regression Model for Distribution Inputs. 2017, 1 .

AMA Style

François Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet. A Gaussian Process Regression Model for Distribution Inputs. . 2017; ():1.

Chicago/Turabian Style

François Bachoc; Fabrice Gamboa; Jean-Michel Loubes; Nil Venet. 2017. "A Gaussian Process Regression Model for Distribution Inputs." , no. : 1.

Preprint
Published: 18 January 2017
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Classification rules can be severely affected by the presence of disturbing observations in the training sample. Looking for an optimal classifier with such data may lead to unnecessarily complex rules. So, simpler effective classification rules could be achieved if we relax the goal of fitting a good rule for the whole training sample but only consider a fraction of the data. In this paper we introduce a new method based on trimming to produce classification rules with guaranteed performance on a significant fraction of the data. In particular, we provide an automatic way of determining the right trimming proportion and obtain in this setting oracle bounds for the classification error on the new data set.

ACS Style

Marina Antolín; Eustasio Del Barrio; Jean-Michel Loubes. A data driven trimming procedure for robust classification. 2017, 1 .

AMA Style

Marina Antolín, Eustasio Del Barrio, Jean-Michel Loubes. A data driven trimming procedure for robust classification. . 2017; ():1.

Chicago/Turabian Style

Marina Antolín; Eustasio Del Barrio; Jean-Michel Loubes. 2017. "A data driven trimming procedure for robust classification." , no. : 1.

Preprint
Published: 17 January 2017
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Classification rules can be severely affected by the presence of disturbing observations in the training sample. Looking for an optimal classifier with such data may lead to unnecessarily complex rules. So, simpler effective classification rules could be achieved if we relax the goal of fitting a good rule for the whole training sample but only consider a fraction of the data. In this paper we introduce a new method based on trimming to produce classification rules with guaranteed performance on a significant fraction of the data. In particular, we provide an automatic way of determining the right trimming proportion and obtain in this setting oracle bounds for the classification error on the new data set.

ACS Style

Marina Antolín; Eustasio Del Barrio; Jean-Michel Loubes. A data driven trimming procedure for robust classification. 2017, 1 .

AMA Style

Marina Antolín, Eustasio Del Barrio, Jean-Michel Loubes. A data driven trimming procedure for robust classification. . 2017; ():1.

Chicago/Turabian Style

Marina Antolín; Eustasio Del Barrio; Jean-Michel Loubes. 2017. "A data driven trimming procedure for robust classification." , no. : 1.

Journal article
Published: 01 January 2017 in Annals of Economics and Statistics
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We propose to study the inverse problem of estimating a distribution observed through an image by a parametric operator. We construct first estimators for the individual parameters of the operators and study their behaviour, then we invert the approximated operator to obtain and estimator of the distribution. The estimation procedure is given by the minimization of a criterion that compares the alignment of the operator to the Wasserstein barycenter of these warped distributions. JEL: C18, C44 / KEY WORDS: Wasserstein Distance, Inverse Problem, Registration.

ACS Style

Eustasio Del Barrio; Jean-Michel Loubes; Bruno Pelletier. An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter. Annals of Economics and Statistics 2017, 229 .

AMA Style

Eustasio Del Barrio, Jean-Michel Loubes, Bruno Pelletier. An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter. Annals of Economics and Statistics. 2017; (128):229.

Chicago/Turabian Style

Eustasio Del Barrio; Jean-Michel Loubes; Bruno Pelletier. 2017. "An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter." Annals of Economics and Statistics , no. 128: 229.

Preprint
Published: 26 August 2015
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We propose a study of a distribution registration model for general deformation functions. In this framework, we provide estimators of the deformations as well as a goodness of fit test of the model. For this, we consider a criterion which studies the Fr{\'e}chet mean (or barycenter) of the warped distributions whose study enables to make inference on the model. In particular we obtain the asymptotic distribution and a bootstrap procedure for the Wasserstein variation.

ACS Style

Eustasio Del Barrio; Hélène Lescornel; Jean-Michel Loubes. A statistical analysis of a deformation model with Wasserstein barycenters : estimation procedure and goodness of fit test. 2015, 1 .

AMA Style

Eustasio Del Barrio, Hélène Lescornel, Jean-Michel Loubes. A statistical analysis of a deformation model with Wasserstein barycenters : estimation procedure and goodness of fit test. . 2015; ():1.

Chicago/Turabian Style

Eustasio Del Barrio; Hélène Lescornel; Jean-Michel Loubes. 2015. "A statistical analysis of a deformation model with Wasserstein barycenters : estimation procedure and goodness of fit test." , no. : 1.

Journal article
Published: 01 January 2015 in Statistica Sinica
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ACS Style

Philippe Fraysse; Hélène Lescornel; Jean-Michel Loubes. A Robbins Monro procedure for the estimation of parametric deformations on random variables. Statistica Sinica 2015, 1 .

AMA Style

Philippe Fraysse, Hélène Lescornel, Jean-Michel Loubes. A Robbins Monro procedure for the estimation of parametric deformations on random variables. Statistica Sinica. 2015; ():1.

Chicago/Turabian Style

Philippe Fraysse; Hélène Lescornel; Jean-Michel Loubes. 2015. "A Robbins Monro procedure for the estimation of parametric deformations on random variables." Statistica Sinica , no. : 1.

Journal article
Published: 25 July 2014 in ESAIM: Probability and Statistics
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We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.

ACS Style

Hélène Lescornel; Jean-Michel Loubes; Claudie Chabriac. Unbiased risk estimation method for covariance estimation. ESAIM: Probability and Statistics 2014, 18, 251 -264.

AMA Style

Hélène Lescornel, Jean-Michel Loubes, Claudie Chabriac. Unbiased risk estimation method for covariance estimation. ESAIM: Probability and Statistics. 2014; 18 ():251-264.

Chicago/Turabian Style

Hélène Lescornel; Jean-Michel Loubes; Claudie Chabriac. 2014. "Unbiased risk estimation method for covariance estimation." ESAIM: Probability and Statistics 18, no. : 251-264.

Journal article
Published: 30 January 2014 in IEEE Transactions on Information Theory
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We present a group lasso procedure for generalized linear models (GLMs) and we study the properties of this estimator applied to sparse high-dimensional GLMs. Under general conditions on the covariates and on the joint distribution of the pair covariates, we provide oracle inequalities promoting group sparsity of the covariables. We get convergence rates for the prediction and estimation error and we show the ability of this estimator to recover good sparse approximation of the true model. Then, we extend this procedure to the case of an elastic net penalty. At last, we apply these results to the so-called Poisson regression model (the output is modeled as a Poisson process whose intensity relies on a linear combination of the covariables). The group lasso method enables to select few groups of meaningful variables among the set of inputs.

ACS Style

Melanie Blazere; Jean-Michel Loubes; Fabrice Gamboa. Oracle Inequalities for a Group Lasso Procedure Applied to Generalized Linear Models in High Dimension. IEEE Transactions on Information Theory 2014, 60, 2303 -2318.

AMA Style

Melanie Blazere, Jean-Michel Loubes, Fabrice Gamboa. Oracle Inequalities for a Group Lasso Procedure Applied to Generalized Linear Models in High Dimension. IEEE Transactions on Information Theory. 2014; 60 (4):2303-2318.

Chicago/Turabian Style

Melanie Blazere; Jean-Michel Loubes; Fabrice Gamboa. 2014. "Oracle Inequalities for a Group Lasso Procedure Applied to Generalized Linear Models in High Dimension." IEEE Transactions on Information Theory 60, no. 4: 2303-2318.

Journal article
Published: 06 December 2013 in Statistical Methods & Applications
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In this paper, we propose a data-driven model selection approach for the nonparametric estimation of covariance functions under very general moments assumptions on the stochastic process. Observing i.i.d replications of the process at fixed observation points, we select the best estimator among a set of candidates using a penalized least squares estimation procedure with a fully data-driven penalty function, extending the work in Bigot et al. (Electron J Stat 4:822–855, 2010). We then provide a practical application of this estimate for a Kriging interpolation procedure to forecast rainfall data.

ACS Style

Rolando Biscay Lirio; Dunia Giniebra Camejo; Jean-Michel Loubes; Lilian Muñiz Alvarez. Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data. Statistical Methods & Applications 2013, 23, 149 -174.

AMA Style

Rolando Biscay Lirio, Dunia Giniebra Camejo, Jean-Michel Loubes, Lilian Muñiz Alvarez. Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data. Statistical Methods & Applications. 2013; 23 (2):149-174.

Chicago/Turabian Style

Rolando Biscay Lirio; Dunia Giniebra Camejo; Jean-Michel Loubes; Lilian Muñiz Alvarez. 2013. "Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data." Statistical Methods & Applications 23, no. 2: 149-174.

Article
Published: 01 June 2013 in Probability Theory and Related Fields
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In this paper, using spectral theory of Hilbertian operators, we study a special class of Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their asymptotic optimality.

ACS Style

T. Espinasse; F. Gamboa; J.-M. Loubes. Parametric estimation for Gaussian fields indexed by graphs. Probability Theory and Related Fields 2013, 159, 117 -155.

AMA Style

T. Espinasse, F. Gamboa, J.-M. Loubes. Parametric estimation for Gaussian fields indexed by graphs. Probability Theory and Related Fields. 2013; 159 (1-2):117-155.

Chicago/Turabian Style

T. Espinasse; F. Gamboa; J.-M. Loubes. 2013. "Parametric estimation for Gaussian fields indexed by graphs." Probability Theory and Related Fields 159, no. 1-2: 117-155.

Preprint
Published: 01 February 2013
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The paper is devoted to the study of a parametric deformation model of independent and identically random variables. Firstly, we construct an efficient and very easy to compute recursive estimate of the parameter. Our stochastic estimator is similar to the Robbins-Monro procedure where the contrast function is the Wasserstein distance. Secondly, we propose a recursive estimator similar to that of Parzen-Rosenblatt kernel density estimator in order to estimate the density of the random variables. This estimate takes into account the previous estimation of the parameter of the model. Finally, we illustrate the performance of our estimation procedure on simulations for the Box-Cox transformation and the arcsinh transformation.

ACS Style

Philippe Fraysse; Hélène Lescornel; Jean-Michel Loubes. A Robbins-Monro procedure for the estimation of parametric deformations on random variables. 2013, 1 .

AMA Style

Philippe Fraysse, Hélène Lescornel, Jean-Michel Loubes. A Robbins-Monro procedure for the estimation of parametric deformations on random variables. . 2013; ():1.

Chicago/Turabian Style

Philippe Fraysse; Hélène Lescornel; Jean-Michel Loubes. 2013. "A Robbins-Monro procedure for the estimation of parametric deformations on random variables." , no. : 1.