Multivariate Statistics

URL study guide

https://studiegids.vu.nl/en/courses/2025-2026/E_EDS2_MS

Course Objective

The student is able to:understand and wield (a number of) the techniques for dealing with multivariate data structures, as well as their statistical properties, and select the appropriate technique(s) for the empirical data at hand;implement and apply the above techniques to real and simulated data using standard and/or tailor-made computer software;report and interpret the results of the analysis clearly according to academic standards.

Course Content

In this course, students familiarize themselves with a range of statistical techniques used for analyzing multivariate data structures. Topics include:
- multivariate distributions (properties, multivariate normal, multivariate t, Wishart)
- more flexible techniques for multivariate data:mixture modelscopulae
- factor models (dimension reduction techniques): principal components analysis, factor analysis
- classification techniques: clustering. Next to developing a thorough understanding of the concepts and statistical properties of the different techniques, students also apply their knowledge on real data in small teams and individually and report about their findings in an academically professional way.

Teaching Methods

Lectures (4h/week) + Exercises (2hr/week)

Method of Assessment

WE = Written Exam – Individual assessment A1 = Assignment 1 – Assessment in groups of 3 A2 = Assignment 2 – Assessment individually F = Final Grade To pass this course, you need WE>=5.0 and F>=5.5. If WE>=5.0, the final grade is F = 0.65 WE + 0.35 (A1+A2)

Literature

Härdle, W.K., and L. Simar (2019): Applied Multivariate Statistical Analysis. Springer, 5th ed. Available via the VU library (search for “Hardle Simar”)

Recommended background knowledge

Students are familiar withlinear algebra (matrix and vector properties and operations) as taught in the course Linear Algebraproperties of random variables (properties, conditioning, transformations) as taught in the course Introduction to Data Science, Statisticsmaximum likelihood theory and statistical hypothesis testing, as taught in the courses Statistics and Introduction to Data Scienceprogramming and numerical optimization, as taught in the Introduction to Programming and Numerical Methods coursesLinear regression model as taught in Econometrics IThis foreknowledge will be used extensively throughout the course, in particular linear algebra techniques. Students are expected to re-familiarize themselves in case of gaps in these topics.