Advanced Statistics

General Information

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

Lectures Tuesday, 10:00 - 12:00
Exercise Tuesday, 16:00 - 18:00

Exam (open): TBA

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 excursions to causality and/or semiparametric efficiency

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=70331

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.