Non parametric statistics and global sensitivity analysis tools in the study of (tail) dependence

par Cécile Mercadier (Institut Camille Jordan, Université Claude Bernard Lyon 1)

lundi 10 juil. 2023, 14:00 → 16:00 Europe/Paris

Salle Fokko du Cloux

La soutenance se tiendra (en anglais) devant le jury composé de :
M. Patrice BERTAIL (Université Paris Nanterre)
M. John EINMAHL (Tilburg University)
Mme Anne-Laure FOUGÈRES (Université Lyon 1)
M. Bertrand IOOSS (EDF Lab Chatou)
Mme Véronique MAUME-DESCHAMPS (Université Lyon 1)
Mme Clémentine PRIEUR (Université Grenoble Alpes)

 

Abstract:

My research work lies at the interface of extreme value theory, sensitivity analysis, and non-parametric inference. The links between the first two themes are not obvious but their combination has proved fruitful. The aim of extreme value theory is to propose probabilistic models that allow for extrapolation of a phenomenon to rarely observed values. It allows goodness-of-fit tests, statistical evaluations, and comparison of the efficiency of different procedures. Finally, applying it enables us to improve our understanding of various environmental or financial phenomena, for example.

At the heart of my habilitation thesis is the stable tail dependence function, which provides a complete characterization of the asymptotic dependence structure. Its study involves interesting mathematical concepts, such as multivariate monotonicity, homogeneity, or spectral representation. Furthermore, it becomes additive on asymptotically independent components. This search for additivity is also explored through superset importance indices in global sensitivity analysis. In particular, the Hoeffding-Sobol decomposition has allowed me to introduce new concepts such as tail superset importance coefficients and the tail dependograph. More generally, the analysis of functional decompositions using commutative and idempotent operators yield a better understanding of the similarities and differences between Hoeffding-Sobol and Möbius decompositions. This has led to the emergence of a general framework for analyzing various statistical dependence hypotheses.