Multivariate statistics
Summary
Multivariate statistics refers to data in vector form. The main objective is to uncover the associations between the components of the vectors. The course introduces the major types of statistical methodology for this purpose as well as some applications to quantitative risk management.
Content
- Reminder about random vectors.
- The multivariate normal distribution.
- Multivariate normal mixture distributions and applications to risk management.
- Spherical and elliptical distributions.
- Copulas (theoretical background and examples).
- Dependence measures (linear correlation, rank correlation, coefficients of tail dependence), asymptotic dependence and independence. Applications to risk management.
- Principal component analysis.
- Canonical correlation analysis.
- Linear discriminant analysis.
- The Wishart and Hotelling T² distributions.
- Multivariate hypothesis testing.
- Basics about graphical models, directed acyclic graphs and Markov random fields.
Learning Prerequisites
Required courses
Solid knowledge in Probability Theory and Statistics.
Learning Outcomes
By the end of the course, the student must be able to:
- Manipulate the multivariate normal distribution and some of its extensions.
- Expound the main results about copulas and apply some models of copulas.
- Expound and apply the main dependence measures.
- Apply a canonical correlation analysis to some concrete cases.
- Apply a principal component analysis to some concrete cases.
- Perform basic multivariate hypothesis tests.
- Demonstrate a basic understanding of linear discriminant analysis.
- Demonstrate a basic understanding of graphical models theory.
- Demonstrate his/her understanding of the main mathematical concepts/proofs of the course.
- Justify the use of a method for a particular data set, especially in applications involving quantitative risk management.
Teaching methods
Lecture ex cathedra using slides as well as the blackboard (especially for proofs). Examples/exercices presented/solved at the blackboard.
Assessment methods
Written examination.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Notes/Handbook
The slides will be available on Moodle.
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks