Multivariate Statistical Methods

Aim

After completion of the course, the student should be able to: - analyze multivariate data by using appropriate multivariate models,

• account for mathematical models related to various multivariate methods and derive theoretical results from these models, - apply hypothesis testing and large sample theory to assess the credibility of the results obtained by multivariate models,
• use computer simulations to solve multivariate statistical problems,
• account for different types of covariance structures and their impact on interpretation, - apply multivariate methods for dimension reduction.

Content

The course comprises the mathematical theory for the multivariate normal distribution and its related distributions, as well as the practical application of this theory to a range of multivariate statistical model and inference problems in statistics, machine learning and engineering.

The course includes:

• matrix algebra, random vectors and matrices
• multivariate normal distribution, mathematical properties of sampling distributions and large sample theory.
• inference of mean vectors, related hypothesis testing models and confidence regions- principal component analysis and large sample inference
• factor analysis,- canonical correlation analysis and large sample inference,- MANOVA models.