Multivariate Statistical Methods

Aim

This course gives knowledge in multivariate statistical analysis, both theory and methods. The course presents and discuss multivariate sampling distributions, quadratic forms, the Wishart distribution, and its applications in sampling. Focus on the course are multivariate significance tests, profile analysis, MANOVA, linear and bilinear models, multivariate distance measures, discriminant and classification analysis, together with principal component, factor and canonical correlation analysis. These are implemented using appropriate statistical software to analyze data, interpret the results and draw appropriate conclusions. After completing the course, the student should be able to:

• 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;
• derive and understand how to use various multivariate statistical methods presented and discussed in the course, and their limitations;
• implement these methods using an appropriate statistical software package and draw appropriate conclusions.

Content

Results from linear algebra, generalized inverses, Kronecker products. Multivariate normal distribution, some properties and sampling. Quadratic forms, Wishart distribution and applications. Inferences about mean vectors and covariance matrices. Profile analysis, MANOVA, and linear and bilinear models. Supervised learning. Discriminant and classification analysis. Principal components, factor, and canonical correlation analysis. Use of statistical software.