Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Journée du Jeudi 17 Novembre 2022

« Théorèmes limites, Champs aléatoires et U-statistiques»

Université de Rouen Normandie – LMRS UMR 6085

    9h45 - 10h15

Opening
10h15 - 11h15

Florence Merlevède

“Rates of convergence in the CLT for non stationary sequences and application to sequential dynamical systems”

Abstract: This talk is devoted to rates of convergence for minimal distances and for the uniform distance, between the law of partial sums associated with non necessarily stationary sequences and the limiting Gaussian distribution. Applications to non stationary rho-mixing sequences and sequential dynamical systems will be provided. This is a joint work with J. Dedecker and E. Rio.

11h30 - 12h30

Herold Dehling (Colloquium du LMRS)

A test for constancy of the variance under short-range dependence

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini’s mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic, we establish new limit theorems for U-statistics of dependent triangular arrays. We derive the asymptotic distribution of the test statistic under the null hypothesis of a constant variance and show that the test is consistent against a large class of alternatives, including multiple breaks. (Joint work with Roland Fried, Davide Giraudo, Sara Schmidt, and Max Wornowizki

12h30 - 14h30

Lunch
14h30 - 15h20

Jérôme Dedecker

‘’Estimation de la CVaR pour des suites alpha dépendantes’’ 

Résumé : nous étudions les propriétés de l'estimateur empirique de la CVaR (conditional value at risk) obtenu à partir d'une suite strictement stationnaire  satisfaisant des conditions de mélange faible. Nous montrons la consistance de l'estimateur, un théorème limite central, et nous obtenons des vitesses de convergence presque sûres. Nous proposons aussi un intervalle de confiance asymptotique, et nous évaluons ses performances via différents jeux de simulation. Travail en collaboration avec Florence Merlevède.

15h30 - 16h20

Olivier Durieu

‘’Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise’’

Abstract: We will consider a toy model of stochastic process with long-range dependence perturbed by a multiplicative noise. The marginal distributions of both the original process and the noise have regularly-varying tails with indices $\alpha>0$ and $\alpha'>0$, respectively. The original process is taken as the Karlin model with memory parameter $\beta\in(0,1)$, a model of random partition which will be recalled beforehand. Functional limit theorems for the extremes of the model can be investigated and reveal a phase transition. There are three different regimes: signal-dominance ($\alpha<\alpha'\beta$), noise-dominance ($\alpha<\alpha'\beta$), and critical regime ($\alpha=\alpha'\beta$). This is a joint work with Yizao Wang.
16h20 - 16h40

Coffee break

16h40 - 17h30

Davide Giraudo

‘’Deviation inequalities for U-statistics using multi-indexed martingales’’

Abstract : In this talk, we will present a deviation inequality for Banach-valued multi-indexed martingale difference random fields. Using decoupling, we will derive analogous inequalities for U-statistics for independent data. We will present applications to convergence rates in the law of large numbers and functional central limit theorems.