# General Information

This is the course website for **STAT 7200: Multivariate Statistics**. This course aims to provide students with a broad overview of techniques used in multivariate statistical analysis, with an emphasis on *Multivariate Linear Regression* and *Principal Component Analysis*. At the end of the course, students will be able to

- make decisions on how and when to use the techniques discussed in class;
- apply and assess multivariate methods on real data;
- make sound statistical conclusions based on a multivariate analysis.

Moreover, the course aims to make students familiar, or competent, with the `R`

statistical software.

- Instructor: Max Turgeon
- Email: max.turgeon@umanitoba.ca
- Office: 373 Machray Hall
- Website: https://maxturgeon.ca/w20-stat7200/
- Lectures: MWF 9:30 AM–10:20 AM, 344 Helen Glass Centre
- Office Hours:
- Tuesday 9:30AM-11AM
- Wednesday 10:30AM-12PM (i.e. after class)
- By appointment (if necessary)

The course outline can be downloaded here.

## Prerequisites

Consent of the instructor. Good knowledge of linear algebra and mathematical statistics is required.

## Textbook

There is no required textbook for this class. If you are looking for a good reference, I recommend:

- Anderson,
*An Introduction to Multivariate Statistical Analysis*. Wiley (2003). - Muirhead,
*Aspects of Multivariate Statistical Theory*. Wiley (2005). - Johnson & Wichern,
*Applied Multivariate Statistical Analysis*. Prentice Hall (2007). - Fujikoshi, Ulyanov & Shimizu,
*Multivariate Statistics–High-Dimensional and Large-Sample Approximations*. Wiley (2010). - Bilodeau & Brenner,
*Theory of Multivariate Statistics*. Springer (1999).

## Assessments

The assessments for this course include:

- Three (3) assignments;
- One (1) midterm test;
- One (1) final project, which includes a written report and an oral presentation.
- The guidelines for the term project can be found here.

In particular, there is **no final exam**.

# Outline of Topics

The course is expected to cover the following topics:

*Aspects of multivariate analysis*: handling multivariate data, graphical displays, statistical distance*Matrix algebra and random vectors*: eigenvalues and eigenvectors, positive definite matrices, mean vectors, covariance matrices and matrix decompositions*Random Samples*: sample geometry, characterizing random samples*Multivariate normal distribution*: definition and properties, estimation and sampling distributions*Inferences about a mean vector*: Hotelling's T2 and likelihood ratio tests, confidence regions and multiple comparisons*Multivariate linear regression*: multivariate analysis of variance, least squares estimation and inference*Principal Component Analysis*: interpretation and use of principal components*Factor Analysis*: orthogonal factor model, estimation and inference*Canonical Correlation Analysis*: canonical variables and canonical correlations- Graphical models (if time permits)

# Statistical Software

The course will make use of the R statistical software for demonstrating some of the theoretical concepts. Sample codes will be provided to students.

You can download R for free (for Windows, Mac, Linux, and Solaris) from the *Comprehensive R Archive Network* at: https://cran.r-project.org/

For additional resources on R, see here.