5.00 credits
30.0 h
Q1
This learning unit is not open to incoming exchange students!
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
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 ?
- Vectorial and Hilbert space
- The projection theorem
- Mean, variance, covariance, correlation, partial correlation (marginal and conditional)
- Consistency (Fisher)
- Continuous random vector, expectation and conditional expectation
- Normality : marginal, conditional
- Chi2 : Cochran theorem
- Data homogeneity
- Variable association
- 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
