Dr. Vlad Barbu, University of Rouen, France: Statistical inference based on divergence measures

Vă invităm să participați la prezentarea susținută de dr. Vlad Barbu, University of Rouen, France, în cadrul INNODES, 11 iunie 2024, ora 13, sala C404 (cladirea FSEGA) cu titlul:

Statistical inference based on divergence measures

Abstract This presentation is concerned with statistical methodology based on divergence measures. Divergence measures are of great importance in statistical inference, as a measure of dissimilarity between two random phenoma. In the first part of our presentation, we focus on hypothesis testing based on weighted divergences. More precisely, we present a goodness of fit test and a homogeneity test and we study their performance. This type of tests based on weighted divergences allow us to focus on specific subsets of the support without, at the same time, losing the information of the others. With this method we achieve a significantly more sensitive test than the classical ones but with comparable error rates. These tests are first presented in an iid context. Then we give some elements on extensions of the tests to dependent data, governed by Markov or by semi-Markov chains. When considering divergence measures, equally important are their limiting versions, known as divergence rates. In the second part of our presentation, we focus on generalized divergence measures for Markov chains. We consider generalizations of Alpha divergence measure (Amari and Nagaoka, 2000) and Beta divergence measures (Basu et. al, 1998) and investigate their limiting behaviour. We also study the corresponding weighted generalized divergence measures and the associated rates (Beliș and Guiașu, 1968; Guiașu, 1971; Kapur, 1994).

Dr. Barbu holds the position of Associate Professor at the Laboratory of Mathematics Raphaël Salem (LMRS), University of Rouen – Normandy (URN), France. His research interests span semi-Markov processes, hidden semi-Markov models, and entropy measures for stochastic processes. Vlad actively contributes to the field of statistics through modeling and applications in diverse domains.