Le Laboratoire de Probabilités, Statistique et Modélisation, dans sa forme actuelle, a résulté, au 1er janvier 1999, de la fusion de l'ancien Laboratoire de probabilité de l'université Paris 6 avec l'équipe de Probabilités et statistique de l'université Paris Diderot.
Le laboratoire compte environ 70 enseignants-chercheurs permanents, 50 thésards, une équipe administrative de 6 personnes. Il accueille de plus les activités de deux masters deuxième année, ce qui représente plus de 200 étudiants chaque année.
La thématique du laboratoire s'inscrit dans le domaine des mathématiques appliquées et a pour objet la modélisation, la description et l'estimation des phénomènes aléatoires. Les thèmes de recherche abordés ici concernent des domaines très variés et recouvrent aussi bien des mathématiques fondamentales que des applications dans des domaines aussi divers que la médecine, les sciences humaines, l'astrophysique, les assurances ou la finance...
Le laboratoire comprend six équipes :
Date: 1 6 月 2022 - 14:34
Desc: We introduce one-sided versions of Huber's contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation of the mean of the uncorrupted samples (minimum effect) and selection of the corrupted samples (outliers). Regarding estimation of the minimum effect, we derive the minimax risks and introduce estimators that are adaptive with respect to the unknown number of contaminations. The optimal convergence rates differ from the ones in the classical Huber contamination model. This fact uncovers the effect of the one-sided structural assumption of the contaminations. As for the problem of selecting the outliers, we formulate the problem in a multiple testing framework for which the location and scaling of the null hypotheses are unknown. We rigorously prove that estimating the null hypothesis while maintaining a theoretical guarantee on the amount of the falsely selected outliers is possible, both through false discovery rate (FDR) and through post hoc bounds. As a by-product, we address a long-standing open issue on FDR control under equi-correlation, which reinforces the interest of removing dependency in such a setting.
Date: 2 9 月 2011 - 11:32
Desc: We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on more general Gaussian quaternionic random matrix models are also made.
Date: 16 9 月 2016 - 17:04
Desc: [...]
Date: 12 12 月 2011 - 14:52
Desc: We focus on the problems of regression, classification and an inverse problem in finance. We first deal with the regression on a random design problem, with a design taking its values in a Euclidean space and whose distribution admits a density. We prove the optimality of the estimator obtained by localized projections onto a multi-resolution analysis. We then turn to the supervised binary classification problem and prove that the plug-in classifier built upon the above procedure is optimal. Interestingly enough, it is computationally more efficient than alternative plug-in classifiers, which turns out to be a crucial feature in many practical applications. We then focus on the regression on a random design problem, with a design uniformly distributed on the hyper sphere of a Euclidean space. We show how the tight frame of needlets allows to transpose the traditional wavelet regression methods to this new setting. We finally consider the problem of recovering the risk-neutral density from quoted option prices. We show that the singular value decomposition of restricted call and put operators can be computed explicitly and used to tailor a simple quadratic program, which allows to recover a stable estimate of the risk-neutral density.
Date: 11 9 月 2015 - 13:55
Desc: This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the collection of such classes. The analysis builds on the tight characterization of universal redundancy rate in terms of metric entropy by Haussler and Opper (1997) and on a careful analysis of the performance of the AC-coding algorithm. The latter relies on non-asymptotic bounds for maxima of samples from discrete distributions with finite and non-decreasing hazard rate.
U.F.R. Mathématiques
Sophie-Germain
75013 PARIS