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Optimal transportation for multifractal random measures and applications

Rémi Rhodes, Vincent Vargas (2013)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures.

Optimal uncertainty quantification for legacy data observations of Lipschitz functions

T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi, M. Ortiz (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the problem of providing optimal uncertainty quantification (UQ) – and hence rigorous certification – for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter...

Paul Lévy et l’arithmétique des lois de probabilités

Jean Bertoin (2013)

ESAIM: Probability and Statistics

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.

Narayanaswamy Balakrishnan (2007)

Revista Matemática Complutense

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...

Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)

ESAIM: Probability and Statistics

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 inequalities and dimension free concentration of measure

Nathael Gozlan (2010)

Annales de l'I.H.P. Probabilités et statistiques

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...

Polynomial expansions of density of power mixtures

Denys Pommeret (2007)

ESAIM: Probability and Statistics

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.

Poverty measures and poverty orderings.

Miguel A. Sordo, Héctor M. Ramos, Carmen D. Ramosm (2007)

SORT

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.

Currently displaying 741 – 760 of 1158