Stochastics 3

Lecturer: Jan Beyersmann

Exercises:  Regina Stegherr

General Information

Prerequisites

Elementary Probability Calculus, Stochastik I 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.

Contents

The lecture "Stochastics 3" 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 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 In order to participate in the final exam, it is necessary to earn 50% of the points on the exercise sheets.

Exercise Sheets

on Moodle.

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.
• 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.