Domaine d'intérêts

  • Inégalités de concentration, inégalités de déviation
  • Processus empiriques
  • Statistique non paramétrique
  • Sélection de modèles
  • Martingales
  • Chaînes de Markov

Publications

  • Concentration inequalities for suprema of unbounded empirical processes.
    Annales Henri Lebesgue, 2021, Volume 4, pp. 831-861.
    Résumé — PDF — HAL
    Using martingale methods, we obtain some Fuk-Nagaev type inequalities for suprema of unbounded empirical processes associated with independent and identically distributed random variables. We then derive weak and strong moment inequalities. Next, we apply our results to suprema of empirical processes which satisfy a power-type tail condition.
  • About the rate function in concentration inequalities for suprema of bounded empirical processes.
    Stochastic Processes and their Applications, 2019, Vol. 129, No. 10, 3967-3980.
    Résumé — PDF — Journal — HAL
    We provide new deviation inequalities in the large deviations bandwidth for suprema of empirical processes indexed by classes of uniformly bounded functions associated with independent and identically distributed random variables. The improvements we get concern the rate function which is, as expected, the Legendre transform of the suprema of the log-Laplace transform of the pushforward measure by the functions of the considered class (up to an additional corrective term). Our approach is based on a decomposition in martingale together with some comparison inequalities.
  • An exponential inequality for suprema of empirical processes with heavy tails on the left.
    Comptes Rendus Mathématique, 2019, Vol. 357, No. 6, 537-544.
    Résumé — PDF — Journal — HAL
    In this Note, we provide exponential inequalities for suprema of empirical processes with heavy tails on the left. Our approach is based on a martingale decomposition, associated with comparison inequalities over a cone of convex functions originally introduced by Pinelis. Furthermore, the constants in our inequalities are explicit.
  • Comparison inequalities for suprema of bounded empirical processes.
    Electronic Communications in Probability, 2018, Vol. 23, No. 33, 1-7.
    Résumé — PDF — Journal — HAL
    In this Note we provide comparison moment inequalities for suprema of bounded empirical processes. Our methods are only based on a decomposition in martingale and on comparison results concerning martingales proved by Bentkus and Pinelis.
  • Concentration inequalities for separately convex functions.
    Bernoulli, 2018, Vol. 24, No. 4A, 2906-2933.
    Résumé — PDF — Journal — HAL — Errata
    We provide new comparison inequalities for separately convex functions of independent random variables. Our method is based on the decomposition in Doob martingale. However we only impose that the martingale increments are stochastically bounded. For this purpose, building on the results of Bentkus (2008-2010), we establish comparison inequalities for random variables stochastically dominated from below and from above. We illustrate our main results by showing how they can be used to derive deviation or moment inequalities for functions which are both separately convex and separately Lipschitz, weighted empirical distribution functions, suprema of randomized empirical processes and chaos of order two.

Prépublications

  • Left deviation inequalities for suprema of empirical processes.
    Preprint (2018).
    Résumé — PDF — HAL
    In this paper, we provide left deviation inequalities for suprema of unbounded empirical processes associated with independent and identically distributed random variables by means of martingale methods. This work complete a previous paper in which the deviation on the right-hand side of the mean is studied.

Exposés

Thèse