Asymptotic Statistics M2 RI (University of Toulouse, 2026-2027)

Lecturers: Clément Lalanne and Pierre Neuvial (other part of the class)

⚠ Class cancelled on Monday, October 12 Unfortunately, the class of Monday, October 12 is cancelled because of the student protest movement in France. We will see how to make up for this session and will keep you informed.

Overview

This class aims to introduce the main theoretical foundations of asymptotic statistics.

Room: 1TP1 BMIG.

Evaluation

For all students, the final grade is entirely based on the exam.

Lectures

Lecture 1 Introduction and Random Vectors.
Lecture 2 Random Vectors continued.
Lecture 3 Delta Method - Method of Moments.
Lecture 4 Delta Method - Method of Moments continued and M and Z estimators.
Lecture 5
Lecture 6
Lecture 7

References and External Resources

Lecture notes from previous editions of the class by François Bachoc.

Statistics

Asymptotic Statistics by A. W. van der Vaart, 2000.

Measure and Probability Theory

Intégration, Probabilités et Processus Aléatoires by Jean-François Le Gall, 2006: An excellent introduction to measure theory with elements of stochastic processes and conditional expectation.
Probabilités 2 by Jean-Yves Ouvrard, 2009: A detailed treatment of advanced topics in probability theory.
Exercices de probabilités by M. Cottrell, C. Duhamel, V. Genon-Catalot, T. Meyre, 2016.
Concentration Inequalities: A Nonasymptotic Theory of Independence by Stéphane Boucheron, Gábor Lugosi, and Pascal Massart, 2013.

Machine Learning and Learning Theory

Learning Theory from First Principles by Francis Bach, 2024.

Analysis

Cours d'analyse by Jean-Michel Bony, 2001.