Mathematics and Statistics for Economics

Teacher(s)

Oikonomou Rigas; Van Bellegem Sébastien;

Language

English

Prerequisites

Basic background in mathematics

Main themes

For the mathematics part, the themes of matrix algebra, functions, optimization, and difference/differential equations. For the statistics part: multivariate distributions and related concepts. The two parts are linked in particular by matrix algebra.

Learning outcomes

At the end of this learning unit, the student is able to :
1	The purpose is that students learn the most important mathematical and statistical tools needed for advanced courses in macroeconomics, microeconomics and econometrics. The course serves mostly to refresh students' knowledge in certain topics, and to ensure that all students taking the advanced courses have a common mathe-matical and statistical level.

Content

MATHEMATICS
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
1. Data analysis

• What is a data ?
• Fundamental concepts to describe data : distribution, empirical probability, random vector, law of total probability, law of iterated expactation, marginalization, conditionning, independence, missing data
• What is a parameter ?

2. Geometry of data

• Vectorial and Hilbert space
• The projection theorem
• Mean, variance, covariance, correlation, partial correlation (marginal and conditional)
• Consistency (Fisher)

3. Assumption : the Normal world

• Continuous random vector, expectation and conditional expectation
• Normality : marginal, conditional
• Chi2 : Cochran theorem

4. Contingency table (Pearson)

• Data homogeneity
• Variable association

5. Simplification : the asymptotic world

• Weak law of large numbers
• Central limit theorem (iid)

Teaching methods

Methods: Lectures and home works

Evaluation methods

Written exam

Teaching materials

• STATISTICS : Lecture notes by S. Van Bellegem

Faculty or entity

> ECON