Advanced Statistics

Lecturer: Jan Beyersmann

Exercises:  Regina Stegherr

General Information


English, unless all students have sufficient knowledge of German
Lectures 2 h
Exercises 1 h

Lectures in e-learning format on Moodle

Exercise in e-learning format on Moodle

Exam (open): TBA





Elementary Probability Calculus and Statistics, Linear Algebra, Mathematical Statistics and Measure Theory. The level of the course is that of a first year's master course in Mathematics, but 3-year BSc students will also be able to follow the course. Some basic programming knowledge in R would be helpful.



The lecture Advanced Statistics is a fundamental part in any statistical and any Data Science education, covering, in particular, statistical inference in linear models. Linear models are a key discipline in applied statistics, including the modern fields of analytics/prediction 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.

Exercise Sheets

on Moodle.


  • 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.
  • Farawy, 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.


The current (August 2020) planning for the winter term is to have a hybrid semester with a mix of e-learning and, possibly and depending on the pandemic circumstances, on site learning. Details will be announced in due course, but the current expectation is that courses like Advanced Statistics will need to heavily rely on e-learning.