Mathematical Statistics
In mathematical statistics the aim is to analyze data sets (samples) to gain insight on a broader entirety. Students of this course will be introduced to the basics behind the theory of mathematical statistics in a comprehensive introduction. Essential estimation and test methods are presented. These methods will also be implemented in modern software languages accompanied by the application examples which will give students a deeper understanding of the theory. Furthermore, the goal is to teach all fundamentals needed for more advanced statistical purposes such as in biostatistics, actuarial sciences and finance.
Lecture
Lecturer
Prof. Dr. Evgeny Spodarev
Assistant
Viet Hoang
Time and Place
This course is organized entirely on Moodle.
Due to the current pandemic this course is organized entirely online. The following dates for the lectures and exercise sessions can be ignored for now. More information on Moodle.
Lectures
Tuesday, 8-10, N24-H12
Thursday, 10-12, N24-H12
Exercise sessions
Wednesday, 16-18, N24-H14
ECTS
4 hours lecture + 2 hours exercise session (ECTS 9)
Prerequisites
- Elementare Wahrscheinlichkeitsrechnung und Statistik
- Wahrscheinlichkeitstheorie und Stochastische Prozesse
Target Audience
- BSc Mathematik: Wahlpflicht Angewandte Mathematik
- BSc Wirtschaftsmathematik: Wahlpflicht Stochastik/Optimierung/Finanzmathematik
- BSc Mathematische Biometrie: Wahlpflicht Stochastik
- MSc Mathematik: Wahlpflicht Angewandte Mathematik
- MSc Wirtschaftsmathematik: Wahlplficht Stochastik/Optimierung/Finanzmathematik
- MSc Mathematische Biometrie: Wahlpflicht Mathematik und Statistik
- MSc Finance: Wahlpflicht Mathematik
Contents
- Parametric models and fundamental theory
- Exponential families, completeness, sufficiency
- Point estimation
- Properties of estimators (MSE, bias, consistency)
- Best unbiased estimators, Cramer-Rao inequality
- U-statistics, confidence intervals
- Hypothesis testing
- Density estimation or linear models (introduction)
Lecture Notes
See Moodle.
Exercise Sheets
See Moodle.
Exam
To participate in the final exam at least 50% of the homework points need to be achieved. Further information on Moodle.
Registration for the exam needs to be completed four days in advance of the exam date (only possible if the prerequisite for the exam is passed).
Literature
- P. Bickel, K. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Prentice Hall
- G. Casella, R.L. Berger, Statistical Inference, Duxbury
- Lehmann, E. L., Casella, G. (2006). Theory of point estimation. Springer.
- Lehmann, E. L., Romano, J. P. (2005). Testing statistical hypotheses. Springer.
- Rüschendorf, L (2014). Mathematische Statistik. Springer.
Other useful literature to this course can be found in the Semesterapparat.