Mathematics and Statistics for Economics
[ECON2500]
[30h] 5 crédits
Enseignants : Luc Bauwens, Julio Davila Muro
Langue d'enseignement : Anglais
Niveau : Second cycle
Objectifs (en termes de compétences)
Objet de l'activité (principaux thèmes à aborder)
The two parts are linked in particular by matrix algebra.
Résumé : Contenu et Méthodes
Matrix algebra (inverse, rank, derivatives, eigenvalues, diagonalization and factorization, quadratic forms). Met-ric and topological spaces, vector spaces. Real functions on Rn (continuity, concavity, differentiability, Taylor expansion, mean value theorem, implicit function theorem). Static optimization (constrained and uncon-strained). Difference and differential equations (steady states, stability).
Statistics:
Multivariate distributions: joint, marginal and conditional distributions, (conditional) moments (variance-covariance matrices), independence in probability and linear independence. Law of iterated expectations. Transformation of random vectors. Multivariate normal distribution.
Quadratic forms in normal vectors and related distributions (Student, chi-squared, Fisher)
Methods:
Lectures and home works
Autres informations (Pré-requis, Evaluation, Support, ...)
Other information (prerequisite, evaluation, course materials, ...):
Basic background in mathematics.
Written exam.