# Coursebooks

## Robust and nonparametric statistics

English

#### Remarque

Cours donné en alternance sur deux ans (pas donné en 2018-19)

#### Summary

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 theories.

#### Content

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
• U-statistics
• 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
• Wavelets

#### Learning Prerequisites

##### Required courses

Introduction to Probability, Introduction to Statistics

#### Learning Outcomes

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.

#### Transversal skills

• Assess one's own level of skill acquisition, and plan their on-going learning goals.
• Manage priorities.

#### Teaching methods

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.

Oral exam.

#### Resources

##### Bibliography

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).

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German