Mathematical Statistics
Undergraduate course, University of Copenhagen, Department of Mathematics, 2019
Description of the course
The course covers fundamental elements of statistical theory and methods, including concepts like statistical models, likelihood, estimation, confidence intervals, hypothesis testing, linear regression, generalized linear models, and asymptotic theory.
We focus particularly on the theory of the general linear normal model in finite-dimensional real vector spaces. This abstract mathematical framework allows us to present geometric formulations of key results about the distribution of estimators and test statistics.
The rest of the course demonstrates the advantages of this abstract understanding by exploring simple applications like linear regression and one- and two-way analysis of variance, before moving on to more complex multi-factor models (k-way ANOVA). These models help address general statistical issues, such as interpretation, validation, and model selection, by providing explicit solutions.
Finally, we extend the linear normal model to random effects models (mixed models, variance component models), which arise when experimental design induces more complex dependencies between the data. The course emphasizes hands-on practice in selecting the appropriate statistical model for real-world data.
Capacity
Contributed as a Teaching Assistant. The course was taught by Steffen Lauritzen and Anders Tolver