PhD Oral Exam - Magloire Loudegui Djimdou, Mathematics

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

In this thesis, we develop inference procedures for copula-based models of bivariate dependence. We first investigate the distribution of Kendall’s functions for joint survivors since Kendall’s functions are important for identifying Archimedean copula models. We then provide two estimators for the generator of an Archimedean copula. We also propose a plug-in estimator for Kendall’s tau and a maximum pseudo-likelihood estimation for the copula model parameters in cases where the survival times are subject to bivariate random censoring. These tests are based on the usual (univariate) Kaplan-Meier estimator and a recently proposed estimator for the bivariate case.