Advanced Statistics

Lecturer: Jan Beyersmann

Exercises:  Judith Vilsmeier

General Information

Prerequisites

A class on elementary probability theory and statistics, and measure theory. The level of the course is that of a first year's master course in one of the mathematical programs, but 3-year BSc students will also be able to follow the course. Some basic programming knowledge in R would be helpful.

Contents

The lecture "Advanced Statistics" is a fundamental part in statistical education, covering, in particular, estimation and testing in linear models. Linear models are a key discipline in applied statistics, including the modern fields of analytics, prediction, data science and causality. Topics covered include:

• multivariate normal distribution
• random quadratic forms
• least-squares- and BLUE-estimators
• Analysis of Variance (ANOVA)
• regression analysis
• prediction and causality

Lecture and exercises will combine a thorough mathematical study of linear models theory with more applied aspects, the latter also using R.

Exam TBA

Exercise Sheets and any further information

on Moodle.

https://moodle.uni-ulm.de/course/view.php?id=43212

Moodle keywort will be announced in the first lecture. 

Literature

• Agresti, A., Foundations of linear and generalized linear models. Wiley Series in Probability and Statistics, 2015.
• Christensen, R., Plane answers to complex questions: the theory of linear models. Springer Science and Business Media, 2011.
• Faraway, J.J., Linear Models with R. CRC Press, 2015.
• Toutenburg, H., Lineare Modelle: Schätzung, Vorhersage, Modellwahl, Mean-Square-Error-Superiorität, Zusatzinformation, fehlende Werte, Datenanalyse, kategorielle Regression, Matrixtheorie. Physica-Verl., 1992.