Concepts and treatment of random vectors

Language

French

Prerequisites

Concepts and tools equivalent to those taught in the UE LSTAT2014: Elements of probability and mathematical statistics

Main themes

Concepts of random vectors, multivariates moments and distributions, dependecies - preparing the student for the concept of dependence (prerequisite for many courses of the Master in Statistics)

Content

Joint probability distributions: discrete, continuous
Marginal distributions, conditional distributions
Independence
Covariance and correlation
Moments (moment generating functions) 
Conditional moments (expectation and variance)
Functions of random vectors, transformations
 Multinomial distribution
Multivariate normal distribution: construction, properties
Theory of multinormal: conditional normal, partial correlation, precision matrix, conditional independence
Other dependence concepts: copulas

Teaching methods

The material will be treated from a theoretical point of view, but also via examples and exercices (including simulations on R).

Evaluation methods

The exam will consist in a written exam, completed by a projet on simulations (with R).

Online resources

Moodle (copies of slides, ...)

Bibliography

Chapitres 4.1-4.4 et 4.7 , 5.1- 5.2 (5.3-5.4) du livre « Applied Multivariate Statistical Analysis » (W. Härdle, L. Simar ; Springer 2007) ;
Chapitres 2.5-2.8, 3.5-3.6, 3.9-3.11 ; 4.1.4 et 4.3 du livre « Mathematical Statistics for Economics and Business” (R. Mittelhammer ; Springer 2013)

Teaching materials

• copies des slides sur Moodle

Faculty or entity

> LSBA