# Fiches de cours

## Multivariate statistics

#### Enseignant(s) :

Koch Erwan Fabrice

English

#### Summary

Multivariate statistics refers to data in vector form. The main objective is to uncover the associations between the components of the vectors. The course introduces the major types of statistical methodology for this purpose as well as some applications to quantitative risk management.

#### Content

• The multivariate normal distribution and normal mixture distributions.
• Spherical and elliptical distributions.
• The Wishart distribution and estimation of covariance matrices.
• Copulas (theoretical background and examples).
• Dependence measures (linear correlation, rank correlation, coefficients of tail dependence), asymptotic dependence and independence. Applications to risk management.
• Multivariate hypothesis testing.
• Principal component analysis and factor models. Applications to risk management.
• Canonical correlation analysis.
• Basics of linear discriminant analysis.
• Basics about graphical models, directed acyclic graphs and Markov random fields.

#### Learning Prerequisites

##### Required courses

Solid knowledge in Probability Theory and Statistics.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Manipulate the multivariate normal distribution and some of its extensions.
• Expound the main results about copulas and apply some models of copulas.
• Expound and apply the main dependence measures.
• Apply a canonical correlation analysis to some concrete cases.
• Apply a principal component analysis to some concrete cases.
• Perform basic multivariate hypothesis tests.
• Demonstrate a basic understanding of linear discriminant analysis.
• Demonstrate a basic understanding of graphical models theory.
• Demonstrate his/her understanding of the main mathematical concepts/proofs of the course.
• Justify the use of a method for a particular data set, especially in applications involving quantitative risk management.

#### Teaching methods

Lecture ex cathedra using slides as well as the blackboard (especially for proofs). Examples/exercices presented/solved at the blackboard.

#### Assessment methods

Written examination.

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.

#### Supervision

 Office hours No Assistants Yes Forum Yes

#### Resources

No

##### Notes/Handbook

The slides will be available on Moodle.

### Semaine de référence

LuMaMeJeVe
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
En construction

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand