D. Pommeret - Academia.edu (original) (raw)

Papers by D. Pommeret

Research paper thumbnail of A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model

Journal of Computational and Applied Mathematics, 2015

Research paper thumbnail of Data driven smooth test of comparison for dependent sequences

Journal of Multivariate Analysis, 2015

ABSTRACT In this paper we propose a smooth test of comparison for the marginal distributions of s... more ABSTRACT In this paper we propose a smooth test of comparison for the marginal distributions of strictly stationary dependent bivariate sequences. We first state a general test procedure and several cases of dependence are then investigated. The test is applied to both simulated data and real datasets.

Research paper thumbnail of Time-patterns of antibiotic exposure in poultry production—A Markov chains exploratory study of nature and consequences

Preventive Veterinary Medicine, 2007

This article describes the use of Markov chains to explore the time-patterns of antimicrobial exp... more This article describes the use of Markov chains to explore the time-patterns of antimicrobial exposure in broiler poultry. The transition in antimicrobial exposure status (exposed/not exposed to an antimicrobial, with a distinction between exposures to the different antimicrobial classes) in extensive data collected in broiler chicken flocks from November 2003 onwards, was investigated. All Markov chains were first-order chains. Mortality rate, geographical location and slaughter semester were sources of heterogeneity between transition matrices. Transitions towards a 'no antimicrobial' exposure state were highly predominant, whatever the initial state. From a 'no antimicrobial' exposure state, the transition to beta-lactams was predominant among transitions to an antimicrobial exposure state. Transitions between antimicrobial classes were rare and variable. Switches between antimicrobial classes and repeats of a particular class were both observed. Application of Markov chains analysis to the database of the nation-wide antimicrobial resistance monitoring programme pointed out that transition probabilities between antimicrobial exposure states increased with the number of resistances in Escherichia coli strains. #

Research paper thumbnail of Estimators of the generalized variance for nonnormal exponential families

Research paper thumbnail of Invariant Conjugate Analysis for Exponential Families

ABSTRACT There are several ways to parameterize a distribution belonging to an exponential family... more ABSTRACT There are several ways to parameterize a distribution belonging to an exponential family, each one leading to a different Bayesian analysis of the data under standard conjugate priors. To overcome this problem, we propose a new class of conjugate priors which is invariant with respect to smooth reparameterization. This class of priors contains the Jeffreys prior as a special case, according to the value of the hyperparameters. Moreover, these conjugate distributions coincide with the posterior distributions resulting from a Jeffreys prior. Then these priors appear naturally when several datasets are analyzed sequentially and when the Jeffreys prior is chosen for the first dataset. We apply our approach to inverse Gaussian models and propose full invariant analyses of three datasets.

Research paper thumbnail of Orthogonal polynomials and natural exponential families

Test, 1996

There exist several different characterizations of the class of quadratic natural exponential fam... more There exist several different characterizations of the class of quadratic natural exponential families on R, two of which use orthogonal polynomials. In Feinsilver (1986), the polynomials result from the derivation of the probability densities whileMeixner (1934) adopts an exponential generating function. In this paper, we consider multidimensional extensions of their results which still yield quadratic or simple quadratic natural exponential families.

Research paper thumbnail of Data driven smooth test for paired populations

Journal of Statistical Planning and Inference, 2011

ABSTRACT In this paper we propose a smooth test of comparison of two distribution functions. This... more ABSTRACT In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.

Research paper thumbnail of A Characterization of Poisson–Gaussian Families by Convolution-Stability

Journal of Multivariate Analysis, 2002

If the convolution of natural exponential families on Rd is still a natural exponential family, t... more If the convolution of natural exponential families on Rd is still a natural exponential family, then the families are all Poisson–Gaussian, up to affinity. This statement is a generalization of the one-dimensional versions proved by G. Letac (1992, “Lectures on Natural Exponential Functions and Their Variance Functions,” Instituto de Matemática pura e aplicada: Monografias de matemática, 50, Rı́o de Janeiro)

Research paper thumbnail of A study of variable selection using -prior distribution with ridge parameter

Computational Statistics & Data Analysis, 2012

In the Bayesian stochastic search variable selection framework, a common prior distribution for t... more In the Bayesian stochastic search variable selection framework, a common prior distribution for the regression coefficients is the g-prior of Zellner. However there are two standard cases where the associated covariance matrix does not exist and the conventional prior of Zellner cannot be used: if the number of observations is lower than the number of variables (large p and small n paradigm), or if some variables are linear combinations of others. In such situations, a prior distribution derived from the prior of Zellner can be considered by introducing a ridge parameter. This prior is a flexible and simple adaptation of the g-prior and its influence on the selection of variables is studied. A simple way to choose the associated hyper-parameters is proposed. The method is valid for any generalized linear mixed model and particular attention is paid to the study of probit mixed models when some variables are linear combinations of others. The method is applied to both simulated and real datasets obtained from Affymetrix microarray experiments. Results are compared to those obtained with the Bayesian Lasso.

Research paper thumbnail of Estimateurs de la variance généralisée pour des familles exponentielles non gaussiennes

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001

Reçu le 28 août 2000, accepté après révision le 12 décembre 2000)

Research paper thumbnail of Comments on 'Bayesian variable selection for disease classification using gene expression data

Bioinformatics, 2011

ABSTRACT CONTACT: baragatt@iml.univ-mrs.fr.

Research paper thumbnail of A Construction of Lancaster Probabilities with Margins in the Multidimensional Meixner Class

Australian <html_ent glyph="@amp;" ascii="&"/> New Zealand Journal of Statistics, 2000

The well-known Meixner class of probabilities on R has been extended recently to R d . This gener... more The well-known Meixner class of probabilities on R has been extended recently to R d . This generalized Meixner class corresponds to the simple quadratic natural exponential families characterized by . Following , the present paper offers a characterization of the joint probability of a random vector (X, Y ), such that the two variables X and Y on R d belong to the multidimensional Meixner class and fulfil a bi-orthogonality condition involving orthogonal polynomials. The joint probabilities, called Lancaster probabilities, are characterized by two sequences of orthogonal polynomials with respect to the margins and a sequence of expectations of products. Some multivariate probabilities are studied, namely the Poisson-Gaussian and the gamma-Gaussian.

Research paper thumbnail of Comparing UMVU and ML estimators of the generalized variance for natural exponential families

Statistics, 2007

ABSTRACT In this paper we compare the uniformly minimum variance unbiased (UMVU) estimator and ma... more ABSTRACT In this paper we compare the uniformly minimum variance unbiased (UMVU) estimator and maximum likelihood (ML) estimator of the generalized variance in the context of natural exponential families (NEFs) on , d&gt;1. We conjecture that for irreducible NEFs the proportionality holds if and only if the generalized variance has a specific form. In particular, we show that the estimators are proportional in the simple and homogeneous quadratic NEFs and prove that the UMVU estimator is preferable in terms of mean squared error except for the case of multinomial family.

Research paper thumbnail of A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model

Journal of Computational and Applied Mathematics, 2015

Research paper thumbnail of Data driven smooth test of comparison for dependent sequences

Journal of Multivariate Analysis, 2015

ABSTRACT In this paper we propose a smooth test of comparison for the marginal distributions of s... more ABSTRACT In this paper we propose a smooth test of comparison for the marginal distributions of strictly stationary dependent bivariate sequences. We first state a general test procedure and several cases of dependence are then investigated. The test is applied to both simulated data and real datasets.

Research paper thumbnail of Time-patterns of antibiotic exposure in poultry production—A Markov chains exploratory study of nature and consequences

Preventive Veterinary Medicine, 2007

This article describes the use of Markov chains to explore the time-patterns of antimicrobial exp... more This article describes the use of Markov chains to explore the time-patterns of antimicrobial exposure in broiler poultry. The transition in antimicrobial exposure status (exposed/not exposed to an antimicrobial, with a distinction between exposures to the different antimicrobial classes) in extensive data collected in broiler chicken flocks from November 2003 onwards, was investigated. All Markov chains were first-order chains. Mortality rate, geographical location and slaughter semester were sources of heterogeneity between transition matrices. Transitions towards a 'no antimicrobial' exposure state were highly predominant, whatever the initial state. From a 'no antimicrobial' exposure state, the transition to beta-lactams was predominant among transitions to an antimicrobial exposure state. Transitions between antimicrobial classes were rare and variable. Switches between antimicrobial classes and repeats of a particular class were both observed. Application of Markov chains analysis to the database of the nation-wide antimicrobial resistance monitoring programme pointed out that transition probabilities between antimicrobial exposure states increased with the number of resistances in Escherichia coli strains. #

Research paper thumbnail of Estimators of the generalized variance for nonnormal exponential families

Research paper thumbnail of Invariant Conjugate Analysis for Exponential Families

ABSTRACT There are several ways to parameterize a distribution belonging to an exponential family... more ABSTRACT There are several ways to parameterize a distribution belonging to an exponential family, each one leading to a different Bayesian analysis of the data under standard conjugate priors. To overcome this problem, we propose a new class of conjugate priors which is invariant with respect to smooth reparameterization. This class of priors contains the Jeffreys prior as a special case, according to the value of the hyperparameters. Moreover, these conjugate distributions coincide with the posterior distributions resulting from a Jeffreys prior. Then these priors appear naturally when several datasets are analyzed sequentially and when the Jeffreys prior is chosen for the first dataset. We apply our approach to inverse Gaussian models and propose full invariant analyses of three datasets.

Research paper thumbnail of Orthogonal polynomials and natural exponential families

Test, 1996

There exist several different characterizations of the class of quadratic natural exponential fam... more There exist several different characterizations of the class of quadratic natural exponential families on R, two of which use orthogonal polynomials. In Feinsilver (1986), the polynomials result from the derivation of the probability densities whileMeixner (1934) adopts an exponential generating function. In this paper, we consider multidimensional extensions of their results which still yield quadratic or simple quadratic natural exponential families.

Research paper thumbnail of Data driven smooth test for paired populations

Journal of Statistical Planning and Inference, 2011

ABSTRACT In this paper we propose a smooth test of comparison of two distribution functions. This... more ABSTRACT In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.

Research paper thumbnail of A Characterization of Poisson–Gaussian Families by Convolution-Stability

Journal of Multivariate Analysis, 2002

If the convolution of natural exponential families on Rd is still a natural exponential family, t... more If the convolution of natural exponential families on Rd is still a natural exponential family, then the families are all Poisson–Gaussian, up to affinity. This statement is a generalization of the one-dimensional versions proved by G. Letac (1992, “Lectures on Natural Exponential Functions and Their Variance Functions,” Instituto de Matemática pura e aplicada: Monografias de matemática, 50, Rı́o de Janeiro)

Research paper thumbnail of A study of variable selection using -prior distribution with ridge parameter

Computational Statistics & Data Analysis, 2012

In the Bayesian stochastic search variable selection framework, a common prior distribution for t... more In the Bayesian stochastic search variable selection framework, a common prior distribution for the regression coefficients is the g-prior of Zellner. However there are two standard cases where the associated covariance matrix does not exist and the conventional prior of Zellner cannot be used: if the number of observations is lower than the number of variables (large p and small n paradigm), or if some variables are linear combinations of others. In such situations, a prior distribution derived from the prior of Zellner can be considered by introducing a ridge parameter. This prior is a flexible and simple adaptation of the g-prior and its influence on the selection of variables is studied. A simple way to choose the associated hyper-parameters is proposed. The method is valid for any generalized linear mixed model and particular attention is paid to the study of probit mixed models when some variables are linear combinations of others. The method is applied to both simulated and real datasets obtained from Affymetrix microarray experiments. Results are compared to those obtained with the Bayesian Lasso.

Research paper thumbnail of Estimateurs de la variance généralisée pour des familles exponentielles non gaussiennes

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001

Reçu le 28 août 2000, accepté après révision le 12 décembre 2000)

Research paper thumbnail of Comments on 'Bayesian variable selection for disease classification using gene expression data

Bioinformatics, 2011

ABSTRACT CONTACT: baragatt@iml.univ-mrs.fr.

Research paper thumbnail of A Construction of Lancaster Probabilities with Margins in the Multidimensional Meixner Class

Australian <html_ent glyph="@amp;" ascii="&"/> New Zealand Journal of Statistics, 2000

The well-known Meixner class of probabilities on R has been extended recently to R d . This gener... more The well-known Meixner class of probabilities on R has been extended recently to R d . This generalized Meixner class corresponds to the simple quadratic natural exponential families characterized by . Following , the present paper offers a characterization of the joint probability of a random vector (X, Y ), such that the two variables X and Y on R d belong to the multidimensional Meixner class and fulfil a bi-orthogonality condition involving orthogonal polynomials. The joint probabilities, called Lancaster probabilities, are characterized by two sequences of orthogonal polynomials with respect to the margins and a sequence of expectations of products. Some multivariate probabilities are studied, namely the Poisson-Gaussian and the gamma-Gaussian.

Research paper thumbnail of Comparing UMVU and ML estimators of the generalized variance for natural exponential families

Statistics, 2007

ABSTRACT In this paper we compare the uniformly minimum variance unbiased (UMVU) estimator and ma... more ABSTRACT In this paper we compare the uniformly minimum variance unbiased (UMVU) estimator and maximum likelihood (ML) estimator of the generalized variance in the context of natural exponential families (NEFs) on , d&gt;1. We conjecture that for irreducible NEFs the proportionality holds if and only if the generalized variance has a specific form. In particular, we show that the estimators are proportional in the simple and homogeneous quadratic NEFs and prove that the UMVU estimator is preferable in terms of mean squared error except for the case of multinomial family.