# 732A97 Multivariate Statistical Methods

### Course information for 2019/20

#### Course description

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

- 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 732A97_MvStat_Examination_IntegralTable.pdf, 732A97_MvStat_Examination_MathFormulas.pdf).
Active participation in the seminars gives maximum 0.5 bonus points per seminar to the exam. A student who earns the bonus points will add all the points to the exam result in order to reach grade E, D or C, 1.5 point in order to reach grade B and 0.5 points in order to reach grade A. 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

## Schedule (check with Timeedit, in case of conflict Timeedit is correct)

#### Tuesday November 5 13-15 in Vallfarten

Type: Lecture 1
Content: Introduction, visualization, distances. (Chapter 1), Exercise 1.17

#### Wednesday November 6 8-10 in C4

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

#### Tuesday November 12 13-15 in A1

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

#### Thursday November 14 10-12 in Vallfarten

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

#### Friday November 15 15-17 in C2

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

#### Monday November 18 13-15 in KEY1

Type: Lecture 5
Content: Inference about a mean vector (Chapter 5)

#### Tuesday November 19 13-15 in KEY1

Type: Lecture 6
Content: MANOVA (Chapter 6)

#### Friday November 22 15-17 in KEY1

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

#### Sunday November 24 23:59 Deadline for Computer Assignment 1

Submission through LISAM.

#### Monday November 25 10-12 in Planck

Type: Lecture 7
Content: Principal components analysis (Chapter 8)

#### Tuesday November 26 13-15 in Planck

Type: Lecture
Content: Factor analysis (Chapter 9)

#### Friday November 29 15-17 in Planck

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

#### Sunday December 1 23:59 Deadline for Computer Assignment 2

Submission through LISAM.

#### Monday December 2 10-12 in C3

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

#### Tuesday December 3 13-15 in C2

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

#### Friday December 6 15-17 in C3

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

#### Sunday December 8 23:59 Deadline for Computer Assignment 3

Submission through LISAM.

#### Monday December 9 10-12 in I101

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

#### Sunday December 15 23:59 Deadline for Computer Assignment 4

Submission through LISAM.

#### Tuesday January 14 8-12

Content: Written examination

#### Sunday February 2 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.

Page responsible: Krzysztof Bartoszek
Last updated: 2021-01-14