Concepts and treatment of random vectors

lstat2190  2023-2024  Louvain-la-Neuve

Concepts and treatment of random vectors
4.00 credits
15.0 h + 7.5 h
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)
Joint probability distributions: discrete, continuous
Marginal distributions, conditional distributions
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, ...)
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

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Learning outcomes
Master [120] in Data Science : Statistic

Master [120] in Statistics: Biostatistics

Master [120] in Statistics: General

Approfondissement en statistique et sciences des données

Certificat d'université : Statistique et science des données (15/30 crédits)