ABSTRACT
My research is devoted to the derivation of non-asymptotic results in probability and statistics. Basically, this is a question of personal taste: I have been struggling with constants in probability bounds since the very beginning of my career. I was very lucky to learn from the elegant work of Michel Talagrand that the dream of a non-asymptotic theory of independence could actually become reality. Thanks to my long-term collaboration with my colleague and friend Lucien Birge´, I could realize the importance of a non-asymptotic approach to statistics. This led me to follow a singular path, back and forth between concentration inequalities and model selection, that I briefly describe below in this (informal) paper for the 50th anniversary of the COPSS.
