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# MAI0142 Estimation and testing hypotheses in multivariate models /Skattning och hypotesprövning för multivariata modeller

Number of credits: 8 hp

Examiner: Dietrich von Rosen and Martin Singull, Division of Mathematical Statistics, Department of Mathematics, Linköping university.

Course literature: The main literature for the course will be two books

1. Advanced Multivariate Statistics with Matrices by Tonu Kollo and Dietrich von Rosen,
2. Bilinear Regression Analysis - An Introduction by Dietrich von Rosen.

Also, some scientific papers will be considered to cover for the most recent findings in the field.

Aim:

The course is intended to give extended knowledge of the theory and methods in analysing linear and bilinear models and to introduce recent developments in the field. By the end of the course, the student should:

• be able to use appropriate linear and bilinear models to describe and analyse observed data and draw conclusions concerning interesting parameters;
• understand the need and use of structured covariance matrices in statistical inference;
• be familiar with the concepts of high dimensional analyses;
• be able to critically evaluate linear and bilinear models in some real-world applications based on the above context;
• be able to use suitable software (e.g., R or similar) for certain types of statistical analyses.

Course contents:

• Multivariate distributions
• Normal distribution
• Wishart distribution
• Linear models (MANOVA)
• Bilinear models
• Profile analysis
• Inference, i.e., estimation and testing hypotheses
• residual analyses
• structured covariance matrices
• high dimensions analyses
• Analysis of data by using appropriate statistical software, e.g., R or similar.

Organization: Lectures and individual presentations.

Examination: Hand-in assignments and individual presentations.

Prerequisites:  Basic courses in probability theory, statistical inference and linear algebra.

Course webpage

Sidansvarig: karin.johansson@liu.se