Concepts and treatment of random vectors

lstat2190  2022-2023  Louvain-la-Neuve

Concepts and treatment of random vectors
4.00 credits
15.0 h + 7.5 h
Q1
Teacher(s)
von Sachs Rainer;
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)
Learning outcomes

At the end of this learning unit, the student is able to :

determine the joint, marginal and conditional distributions, as well as their associated moments.
 
understand the concepts of dependence quantified by the (partial) correlation and compare them to the case of independence.
 
master classical multivariate distributions such as multinormal and multinomial.
 
perform theoretical calculations by hand and using statistical software.
 
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


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

Title of the programme
Sigle
Credits
Prerequisites
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)