Multivariate statistics

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.

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
  • 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
  • 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: mandatory
  • 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: mandatory

Reference week

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