# TAMS39 -- Course Information

#### Course Aims

This course provides an introduction to multivariate statistical analysis, both theory and methods. The theory discusses multivariate sampling distributions and their characteristic functions, quadratic forms, elliptical distributions, exterior forms, the Wishart distribution and its applications in sampling. The practical side of the course discusses multivariate significance tests, principal component analysis, factor analysis, multivariate distance measures, discriminant analysis, cluster analysis and canonical correlation analysis. These are implemented using appropriate statistical software to analyse data, interpret the results and draw appropriate conclusions. After completing the course the student should be able to:
• Compute the characteristic functions of some well known distributions and use multivariate characteristic functions to investigate properties of various distributions.
• Derive various multivariate sampling distributions and use exterior forms where appropriate to make the necessary changes of variables.
• Understand and be able to use Kronecker products in problems related to the multivariate normal distribution.
• Understand how the Wishart distribution arises in multivariate sampling and how to use it.
• Understand how to use various multivariate statistical methods (for example: test for significant differences between populations, use principal component analysis and factor analysis, discriminant analysis, cluster analysis and canonical correlation analysis)
• Understand the limitations of these multivariate analysis methods.
• Implement these methods using an appropriate statistical software package and draw appropriate conclusions.

#### Organisation

The Lectures give an overview of the theory. During the problem solving Example classes concrete examples, intended to illustrate the theory are given. Three of the example classes are in the computer lab and will give practical experience with implementing and using the methods.

#### Course Contents

Results from Linear Algebra. The characteristic function, the multivariate normal distribution and some properties. Generalised inverses. The Euler Gamma function, the chi squared, F and t distributions. Quadratic forms. Spherical and Elliptical Distributions, multivariate cumulants, skewness, kurtosis. Kronecker products, the Multivariate Gamma function, exterior products. Sampling from a multivariate normal distribution, the Wishart distribution and applications. Inferences about mean vectors. Principal components analysis, factor analysis, discriminant analysis and cluster analysis. Canonical correlation. Other multivariate methods. Use of statistical software.

#### Examination

EXAM Oral examination 4 ECTS
COMP Hand in assignments/project 2 ECTS

Page responsible: martin.singull@liu.se
Last updated: 2019-11-29