Parametric two-point integral inequalities for -time differentiable functions with applications.
Partition-dependent stochastic measures and -deformed cumulants.
Paul Lévy et l’arithmétique des lois de probabilités
Ce court texte reprend un exposé donné le 15 Décembre 2011 au Laboratoire de Probabilités et Modèles Aléatoires, lors d’une journée en hommage à Paul Lévy. On y rappellera comment des considérations sur l’arithmétique des lois de probabilités ont conduit Lévy à étudier les processus à accroissements indépendants.
Permanents, order statistics, outliers, and robustness.
In this paper, we consider order statistics and outlier models, and focus primarily on multiple-outlier models and associated robustness issues. We first synthesise recent developments on order statistics arising from independent and non-identically distributed random variables based primarily on the theory of permanents. We then highlight various applications of these results in evaluating the robustness properties of several linear estimators when multiple outliers are possibly present in the...
Plongement de lois indéfiniment divisibles
Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory
This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = {Fn(x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by...
Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
For stationary Gaussian processes, we obtain the necessary and sufficient conditions for Poincaré inequality and log-Sobolev inequality of process-level and provide the sharp constants. The extension to moving average processes is also presented, as well as several concrete examples.
Poincaré inequalities and dimension free concentration of measure
In this paper, we consider Poincaré inequalities for non-euclidean metrics on ℝd. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and inf-convolution inequalities. Workable sufficient conditions are given...
Poincaré inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups
Poisson random sums of present Values of Continuous Uniform cash flows
Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails.
Polynomial and spline estimators of the distribution function with prescribed accuracy
Dvoretzky-Kiefer-Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well.
Polynomial expansions of density of power mixtures
For any given random variable Y with infinitely divisible distribution in a quadratic natural exponential family we obtain a polynomial expansion of the power mixture density of Y. We approach the problem generally, and then consider certain distributions in greater detail. Various applications are indicated and the results are also applied to obtain approximations and their error bounds. Estimation of density and goodness-of-fit test are derived.
Positive stable laws and M-scheme
Poverty measures and poverty orderings.
We examine the conditions under which unanimous poverty rankings of income distributions can be obtained for a general class of poverty indices. The "per-capita income gap" and the Shorrocks and Thon poverty measures are particular members of this class. The conditions of dominance are stated in terms of comparisons of the corresponding TIP curves and areas.
Présentation de l'«inégalité de Doob» de Métivier et Pellaumail
Preservation of log-concavity on summation
We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these conditions are natural by giving some applications. Firstly, we use our main theorem to give simple proofs of the log-concavity of the Stirling numbers of the second kind and of the Eulerian numbers. Secondly, we prove results concerning the log-concavity of the sum of...
Principes d'invariance pour la probabilité d'un dilaté de l'enveloppe convexe d'un échantillon
Probabilistic derivation of a bilinear summation formula for the Meixner- Pollaczek polynomials.
Probabilistische Metriken auf der Menge der nicht negativen Verteilungsfunktion.