MATH-444 / 5 credits

Teacher: Panaretos Victor

Language: English

## 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.

## 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

No

## Bibliography

• Theodore W. Anderson: Multivariate Analysis, Wiley

## 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
• Type: optional
• 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
• Type: optional
• 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
• Type: optional
• 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
• Type: optional
• 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
• Type: optional

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