Multivariate statistics
Summary
Multivariate statistics focusses on inferring the joint distributional properties of several random variables, seen as random vectors, with a main focus on uncovering their underlying dependence structure. This course offers a broad introduction to its concepts, methods & theory
Content
- Random vectors and random matrices.
- Product moments and covariance Matrices.
- The multivariate Gaussian and elliptical distributions.
- Limit theorems and concentration of measure.
- Coupling and copulas, measures of dependence
- PCA, CCA, and LDA.
- Covariance estimation and hypothesis testing.
- Nonparametric and semiparametric estimation.
- Gaussian graphical models and conditional independence
- Multivariate statistics in high dimensions.
- Introduction to functional data analysis.
Learning Prerequisites
Required courses
A solid introduction to probability (e.g. MATH-230) and statistics (e.g. MATH-240). Basic knowlege of linear models (e.g. MATH-341) is useful but not necessary.
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 concepts in coupling and 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 and objective
Teaching methods
Lecture ex cathedra using slides as well as 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
Bibliography
- Theodore W. Anderson: Multivariate Analysis, Wiley
Ressources en bibliothèque
Notes/Handbook
The slides will be available on Moodle.
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Multivariate statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory