Concentration results on extreme value theory

Since univariate extreme value theory is essentially based on asymptotic theorems, the elaboration of adaptive estimation procedures or oracle inequalities is challenging. The purpose of this thesis is to show how the development of concentration inequalities in extreme value theory allows us to derive oracle type results. } The first chapter gathers the principal results on order statistics, extreme value theory and concentration theory. Chapters 2 and 3 represent a joint work with Stephane Boucheron: the first chapter presents concentration inequalities for order statistics of a sample of random variables; the second chapter deals with the development of an adaptive version of the Hill estimator based on non asymptotic bounds of this estimator. Chapter 4 summarises the work done in collaboration with epidemiologists on the application of extreme value theory to the example of influenza epidemics.