Robust and nonparametric statistics
MATH-441 / 5 credits
Remark: Cours donné en alternance tous les deux ans (pas donné en 2022-23)
In the decades from 1930 to 1950, many rank-based statistics were introduced. These methods were received with much interest, because they worked under weak conditions. Starting in the late 1950, a theory of robustness was added. The course gives an overview of these two approaches to data analysis.
I. Robust Statistics
- Global and local robustness indicators: Breakdown point, influence function
- Hampel's lemma
- Huber's theory: M-estimators, L-estimators
- Robust tests
- Robust regression
II. Linear Rank Tests
- Test of Mann-Whitney-Wilcoxon and general linear rank tests: asymptotic theory, R-estimators
- Rank correlations
- Comparison of tests: Pitman efficacy
- Permutation tests
III. Estimation of smooth functions
- Curve fitting: polynomial regression, splines
- Smoothing: non parametric estimation, degree of smoothness, bias vs. variance, penalization
- Kernel estimators: definition, properties
- Smoothing splines
- Local regression
Introduction to Probability, Introduction to Statistics
By the end of the course, the student must be able to:
- Expound the content of the course.
- Apply the statistical methods explained in the course.
- Sketch the proofs of the theoretical results given in the course.
- Choose the appropriate robust or non parametric methods for a given data analysis problem.
- Differentiate between robust and non-parametric methods.
- Generalize the tools treated in the course to other problems.
- Apply spline and kernel smoothers.
- Apply M-estimatiors in a variety of situations.
- Assess one's own level of skill acquisition, and plan their on-going learning goals.
- Manage priorities.
Ex cathedra lecture and exercises in the classroom
Expected student activities
Do all the exercices. Prepare each week for the course. Participate actively in the course.
Dans le cas de l’art. 3 al. 5 du Règlement de section, l’enseignant décide de la forme de l’examen qu’il communique aux étudiants concernés.
Introduction to the theory of nonparametric statistics by R.H. Randles and D.A. Wolfe, Wiley.
All of nonparametric statistics by L. Wasserman, Springer.
Robust Statistics: The approach based on influence functions by F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, W.A. Stahel, Wiley.
Robust Statistics by P.J. Huber, Wiley (second edition).
Robust Statistics: Theory and Methods by D.R. Martin, M. Salibian-Barrera, R.A. Maronna, V.J. Yohai, Wiley.
Ressources en bibliothèque
- Introduction to the theory of nonparametric statistics / Randles & Wolfe
- All of nonparametric statistics / Wasserman
- Robust Statistics / Martin & al.
- Robust Statistics / Hampel & al.
- Robust Statistics / Huber
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Robust and nonparametric statistics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks