Course description

This is the course page for the course in Multivariate Statistical Methods.

The information and hyperlinks for 2025 are being updated at the moment. Hence, not all information might be correct.

The first course occasion will be in A302 on Monday 2025-11-10 13:15-15 Lecture!

This is a traditional course in multivariate statistical methods, covering the multivariate normal distribution with inference of mean vectors, principal component analysis, factor analysis and canonical correlation analysis. The course requires good knowledge of matrix algebra and undergraduate courses in statistical inference and linear statistical models.

The course is intended for students in the Masters program Statistics and Data Mining as a profile course in Statistics.

Course literature

- Course textbook: Applied Multivariate Statistical Analysis by R.A. Johnson and D.W. Wichern, Pearson New International Edition/Sixth Edition, ISBN 9781292024943.
- Auxillary book: An Introduction to Applied Multivariate Analysis with R by B. Everitt and T. Hothorn, First Edition, ISBN 978-1-4419-9649-7
- Little Book of R for Multivariate Analysis

Useful links

- Multivariate Statistics: Exercises and Solutions

Exam and bonus point system (possibly subject to change within November depending how the seminars work out)

The examination consists of a written exam with max score 20 points and grade limits:
A : 18p, B: 16p, C: 14p, D: 12p, E: 10p.
You are allowed to bring a pocket calculator to the exam. On the exam you will be allowed to have one double sided A4 page of own notes (hand-written). Also alongside the exam I will distribute the tables of the normal, t, chisq2 and F distributions (the Appendix to the textbook). You will be also provided with a table on integrals and mathematical formulae (files 732A88_MvStat_Examination_IntegralTable.pdf, 732A88_MvStat_Examination_MathFormulas.pdf). These materials can be downloaded from here

Previous exams can be found here.

Active participation in the seminars gives maximum 0.5 bonus points per seminar to the exam. Active participation means that a student comes prepared to the seminar session with all the given day's exercises, correctly solves an exercise on the board, is able to answer questions about the presented solution and is able to give help and comments to the classmates' presented solutions

Hand-in assignments

The course contains 4 assignments that all are mandatory.

Labs are to be done in groups. Groups will be setup at the first classes. Once groups are established the submissions will be open in LISAM. The labs can be downloaded from this webpage. Students must discuss their lab solutions in a group and compile a collaborative report showing the results and the code. Attention: there is a deadline for such a report! The document should clearly state the names of the students that participated in its compilation. This report should be submitted via LISAM as a .PDF with accompanying R scripts (alternatively in case of problems emailed to one of the responsible staff ) before the report deadline.

The solution should contain all used code.

The file should be named Group X.pdf where X is the group number. Please also include your names in the report.

The collaborative reports are corrected and graded by the teacher. A student is PASSED on the lab if the group report is PASSED.

All group members have to contribute to, understand and be able to explain all aspects of the work. In case some member(s) of a group do not contribute equally this has to be reported and in this situation a formal group work contract will be signed, s tipulating the consequences for further unequal contributions.

If you miss the deadline for a lab solution, you must submit the solution anyway, and in this case some penalty assignments may also be given.
There is a second deadline of 23:59 2 February 2026 for submitting corrections for all the hand-ins.
There is a final deadline of 23:59 2 March 2026 for all the hand-ins. After this date NO submissions nor corrections will be accepted.

Late submissions will result in penalty assignments!

Submission is done through LISAM or via email to lab assistants.

ALL submissions will be CHECKED through URKUND for plagarism (also with respect to past labs)!

Monday 10 November 2025 13:15-15 in A302

Type: Lecture 1
Content: Introduction, visualization, distances. (Chapter 1), Exercise 1.17
Definition of distance.
Code for lecture part 1.
Code for lecture part 2.

Friday 14 November 2025 13:15-15 in A302

Type: Lecture 2
Content: Random vectors, sample geometry (Chapter 2 Int. Ed., Chapter 3 Ed. 6)

Monday 17 November 2025 13:15-15 in A302

Type: Lecture 3
Content: Matrix algebra (Chapter 3 Int. Ed., Chapter 2 Ed. 6)

Wednesday 19 November 2025 08:15-10 in A302

Type: Seminar 1
Content: Exercises (Int. Ed.) 2.5, 2.6, 2.8, 2.9, 3.26, 3.27, 3.35; (Ed. 6) 3.5, 3.6, 3.8, 3.9, 2.26, 2.27, 2.35

Friday 21 November 2025 13:15-15 in S25

Type: Lecture 4
Content: Multivariate normal distributon (Chapter 4)

Monday 24 November 2025 13:15-15 in A302

Type: Lecture 5
Content: Inference about a mean vector (Chapter 5)
Summary of tests for equal means.

Wedensday 26 November 2025 08:15-10 in S27

Type: Seminar 2
Content: Exercises (Int. Ed.) 3.2, 3.7, 4.2-4.5, 4.21, 4.22; (Ed. 6) 2.2, 2.7, 4.2-4.5, 4.21, 4.22

Friday 28 November 2025 13:15-15 in A302

Type: Lecture 6
Content: MANOVA (Chapter 6)
Code for lecture.

Monday 1 December 2025 13:15-15 in A302

Type: Lecture 7
Content: Principal components analysis (Chapter 8)
Additional material for lecture.
Code for lecture.

Wednesday 3 December 2025 08:15-10 in S35

Type: Seminar 3
Content: Exercises 5.1, 5.3, 5.4a, 5.7

Friday 5 December 2025 13:15-15 in A302

Type: Lecture 8
Content: Factor analysis (Chapter 9)

Monday 8 December 2025 13:15-15 in Auger

Type: Lecture 9
Content: Canonical correlation analysis (Chapter 10)

Wednesday 10 December 2025 08:15-10 in A302

Type: Seminar 4
Content: Exercises 6.5, 6.8, 6.19, 6.22, 8.4, 8.6, 8.10

Friday 12 December 2025 13:15-15 in S27

Type: Lecture 10
Content: Multidimensional scaling (Chapter 12.6, Chapter 4 in Everitt, Hothorn), Exercise: 4.1 (Everitt, Hothorn)

Wednesday 15 December 2025 13:15-15 in Avogadro

Type: Seminar 5
Content: Exercises 9.10, 9.11, 9.19, 10.2, 10.12

Wednesday 14 January 2026 8-12

Content: Written examination

Monday 2 February 2026 23:59

Content: Deadline for corrections all assignments.

Monday 2 March 2026 23:59

Content: Final deadline for all assignments.
After this date no submissions nor corrections will be considered and you will have to redo the missing labs next year.