Christophe Ley - Academia.edu (original) (raw)

Papers by Christophe Ley

Journal of Statistical Planning and Inference, 2015

ABSTRACT We propose a new testing procedure about the tail weight parameter of multivariate Stude... more ABSTRACT We propose a new testing procedure about the tail weight parameter of multivariate Student distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but outperforms the latter by its flexibility and simplicity: indeed, our approach allows to estimate the location and scatter nuisance parameters by any root- consistent estimators, hereby avoiding numerically complex maximum likelihood estimation. The finite-sample properties of our test are analyzed in a Monte Carlo simulation study, and we apply our method on a financial data set. We conclude the paper by indicating how to use this framework for efficient point estimation.

We inscribe Stein's density approach for discrete distributions in a new, flexible framework, her... more We inscribe Stein's density approach for discrete distributions in a new, flexible framework, hereby extending and unifying a large portion of the relevant literature. We use this to derive a Stein identity whose power we illustrate by obtaining a wide variety of so-called inequalities between probability metrics and information functionals. Whenever competitor inequalities are available in the literature, the constants in ours are better. We also argue that our inequalities are local versions of the famous Pinsker inequality.

It is a well-known fact that multivariate Student t distributions converge to multivariate Gaussi... more It is a well-known fact that multivariate Student t distributions converge to multivariate Gaussian distributions as the number of degrees of freedom ν tends to infinity, irrespective of the dimension k ≥ 1. In particular, the Student's value at the mode (that is, the normalizing constant obtained by evaluating the density at the center) c ν,k =

We construct two different Stein characterizations of discrete distributions and use these to pro... more We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.

We generalize the so-called density approach to Stein characterizations of probability distributi... more We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information.

We tackle the classical two-sample spherical location problem for directional data by having reco... more We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical linear multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests, which we then turn into semi-parametric ones in two distinct ways. First, by using a studentization argument; this leads to so-called pseudo-FvML tests. Second, by resorting to the invariance principle; this leads to efficient rank-based tests. Within each construction, the semi-parametric tests inherit optimality under a given distribution (the FvML in the rst case, any rotationally symmetric one in the second) from their parametric counterparts and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the nite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simu...

We provide a new perspective on Stein's so-called density approach by introducing a new opera... more We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein identity which we use to derive information inequalities in terms of what we call the \emph{generalized Fisher information distance}. We provide explicit bounds on the constants appearing in these inequalities for several important cases. We conclude with a comparison between our results and known results in the Gaussian case, hereby improving on several known inequalities from the literature.

Annals of the Institute of Statistical Mathematics, 2015

Journal of Multivariate Analysis, 2015

Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in ... more Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in directional statistics, involve a location parameter θ θ θ that indicates the direction of the symmetry axis. The most classical way of addressing the spherical location problem H 0 : θ θ θ = θ θ θ 0 , with θ θ θ 0 a fixed location, is the so-called Watson test, which is based on the sample mean of the observations. This test enjoys many desirable properties, but its implementation requires the sample size n to be large compared to the dimension p. This is a severe limitation, since more and more problems nowadays involve high-dimensional directional data (e.g., in genetics or text mining). In this work, we therefore introduce a modified Watson statistic that can cope with high-dimensionality. We derive its asymptotic null distribution as both n and p go to infinity. This is achieved in a universal asymptotic framework that allows p to go to infinity arbitrarily fast (or slowly) as a function of n. We further show that our results also provide high-dimensional tests for a problem that has recently attracted much attention, namely that of testing that the covariance matrix of a multinormal distribution has a "θ θ θ 0 -spiked" structure. Finally, a Monte Carlo simulation study corroborates our asymptotic results.

Wiley StatsRef: Statistics Reference Online, 2014

Annals of the Institute of Statistical Mathematics, 2014

introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry... more introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry about the origin (equivalently, about an arbitrary specified center). His procedure first reorders the observations according to their absolute values, then rejects the null when the number of runs in the resulting series of signs is too small. This test is universally consistent and enjoys nice robustness properties, but is unfortunately limited to the univariate setup. In this paper, we extend McWilliams' procedure into tests of bivariate central symmetry. The proposed tests first reorder the observations according to their statistical depth in a symmetrized version of the sample, then reject the null when an original concept of simplicial runs is too small. Our tests are affine-invariant and have good robustness properties. In particular, they do not require any finite moment assumption. We derive their limiting null distribution, which establishes their asymptotic distribution-freeness. We study their finite-sample properties through Monte Carlo experiments, and conclude with some final comments.

... 50, Avenue Roosevelt CP 114, 1050, Bruxelles, Belgique chrisley@ulb.ac.be yswan@ulb.ac. be 2 ... more ... 50, Avenue Roosevelt CP 114, 1050, Bruxelles, Belgique chrisley@ulb.ac.be yswan@ulb.ac. be 2 EQUIPPE, Université Lille 3, Domaine universitaire du pont de bois, Rue du barreau 59653 Villeneuve d'Ascq cedex, France baba.thiam@univ-lille3.fr thomas.verdebout@univ ...

... Sports II Yves Dominicy∗, Christophe Ley† and Yvik Swan‡ ... Research supported by Mandatde C... more ... Sports II Yves Dominicy∗, Christophe Ley† and Yvik Swan‡ ... Research supported by Mandatde Chargé de Recherches of the Fonds National de la Recherche Scien-tifique, Communauté française de Belgique. 1 Page 2. ... tennis is, to say the least, scant. ...

Journal of Statistical Planning and Inference, 2015

ABSTRACT We propose a new testing procedure about the tail weight parameter of multivariate Stude... more ABSTRACT We propose a new testing procedure about the tail weight parameter of multivariate Student distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but outperforms the latter by its flexibility and simplicity: indeed, our approach allows to estimate the location and scatter nuisance parameters by any root- consistent estimators, hereby avoiding numerically complex maximum likelihood estimation. The finite-sample properties of our test are analyzed in a Monte Carlo simulation study, and we apply our method on a financial data set. We conclude the paper by indicating how to use this framework for efficient point estimation.

We inscribe Stein's density approach for discrete distributions in a new, flexible framework, her... more We inscribe Stein's density approach for discrete distributions in a new, flexible framework, hereby extending and unifying a large portion of the relevant literature. We use this to derive a Stein identity whose power we illustrate by obtaining a wide variety of so-called inequalities between probability metrics and information functionals. Whenever competitor inequalities are available in the literature, the constants in ours are better. We also argue that our inequalities are local versions of the famous Pinsker inequality.

It is a well-known fact that multivariate Student t distributions converge to multivariate Gaussi... more It is a well-known fact that multivariate Student t distributions converge to multivariate Gaussian distributions as the number of degrees of freedom ν tends to infinity, irrespective of the dimension k ≥ 1. In particular, the Student's value at the mode (that is, the normalizing constant obtained by evaluating the density at the center) c ν,k =

We construct two different Stein characterizations of discrete distributions and use these to pro... more We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.

We generalize the so-called density approach to Stein characterizations of probability distributi... more We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information.

We tackle the classical two-sample spherical location problem for directional data by having reco... more We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical linear multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests, which we then turn into semi-parametric ones in two distinct ways. First, by using a studentization argument; this leads to so-called pseudo-FvML tests. Second, by resorting to the invariance principle; this leads to efficient rank-based tests. Within each construction, the semi-parametric tests inherit optimality under a given distribution (the FvML in the rst case, any rotationally symmetric one in the second) from their parametric counterparts and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the nite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simu...

We provide a new perspective on Stein's so-called density approach by introducing a new opera... more We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein identity which we use to derive information inequalities in terms of what we call the \emph{generalized Fisher information distance}. We provide explicit bounds on the constants appearing in these inequalities for several important cases. We conclude with a comparison between our results and known results in the Gaussian case, hereby improving on several known inequalities from the literature.

Annals of the Institute of Statistical Mathematics, 2015

Journal of Multivariate Analysis, 2015

Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in ... more Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in directional statistics, involve a location parameter θ θ θ that indicates the direction of the symmetry axis. The most classical way of addressing the spherical location problem H 0 : θ θ θ = θ θ θ 0 , with θ θ θ 0 a fixed location, is the so-called Watson test, which is based on the sample mean of the observations. This test enjoys many desirable properties, but its implementation requires the sample size n to be large compared to the dimension p. This is a severe limitation, since more and more problems nowadays involve high-dimensional directional data (e.g., in genetics or text mining). In this work, we therefore introduce a modified Watson statistic that can cope with high-dimensionality. We derive its asymptotic null distribution as both n and p go to infinity. This is achieved in a universal asymptotic framework that allows p to go to infinity arbitrarily fast (or slowly) as a function of n. We further show that our results also provide high-dimensional tests for a problem that has recently attracted much attention, namely that of testing that the covariance matrix of a multinormal distribution has a "θ θ θ 0 -spiked" structure. Finally, a Monte Carlo simulation study corroborates our asymptotic results.

Wiley StatsRef: Statistics Reference Online, 2014

Annals of the Institute of Statistical Mathematics, 2014

introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry... more introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry about the origin (equivalently, about an arbitrary specified center). His procedure first reorders the observations according to their absolute values, then rejects the null when the number of runs in the resulting series of signs is too small. This test is universally consistent and enjoys nice robustness properties, but is unfortunately limited to the univariate setup. In this paper, we extend McWilliams' procedure into tests of bivariate central symmetry. The proposed tests first reorder the observations according to their statistical depth in a symmetrized version of the sample, then reject the null when an original concept of simplicial runs is too small. Our tests are affine-invariant and have good robustness properties. In particular, they do not require any finite moment assumption. We derive their limiting null distribution, which establishes their asymptotic distribution-freeness. We study their finite-sample properties through Monte Carlo experiments, and conclude with some final comments.

... 50, Avenue Roosevelt CP 114, 1050, Bruxelles, Belgique chrisley@ulb.ac.be yswan@ulb.ac. be 2 ... more ... 50, Avenue Roosevelt CP 114, 1050, Bruxelles, Belgique chrisley@ulb.ac.be yswan@ulb.ac. be 2 EQUIPPE, Université Lille 3, Domaine universitaire du pont de bois, Rue du barreau 59653 Villeneuve d'Ascq cedex, France baba.thiam@univ-lille3.fr thomas.verdebout@univ ...

... Sports II Yves Dominicy∗, Christophe Ley† and Yvik Swan‡ ... Research supported by Mandatde C... more ... Sports II Yves Dominicy∗, Christophe Ley† and Yvik Swan‡ ... Research supported by Mandatde Chargé de Recherches of the Fonds National de la Recherche Scien-tifique, Communauté française de Belgique. 1 Page 2. ... tennis is, to say the least, scant. ...