Overview
This class aims to introduce the main theoretical foundations of asymptotic statistics.
Asymptotic Statistics M2 RI (University of Toulouse, 2025-2026)
Lecturers: Clément Lalanne and Pierre Neuvial (other part of the class)Evaluation
For all students, the final grade is entirely based on the exam.
Lectures
- Lecture 1 Introduction and Random Vectors 1 (notes).
- Lecture 2 Random Vectors 1 continued and Random Vectors 2 (notes).
- Lecture 3 Delta Method and Method of Moments (notes).
- Lecture 4 M and Z estimators (notes).
- Lecture 5 Bracketing Numbers (notes).
- Lecture 6 Asymptotic Normality of Z Estimators (notes).
- Lecture 7 Maximum Likelihood and exercises.
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
Analysis
- Cours d'analyse by Jean-Michel Bony, 2001.