Modul

The module will be completed by an oral exam (approx. 30 min).

By the end of the course, students will

• know the basic concepts of mathematical statistics,
• be able to apply them independently to simple problems and examples,
• know specific probabilistic techniques and be able to use them for the mathematical analysis of estimation and test procedures,
• know the asymptotic behavior of maximum likelihood estimators and the generalized likelihood ratio for parametric test problems.

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The course covers basic concepts of mathematical statistics, in particular the finite optimality theory of estimators and tests, and the asymptotic behavior of estimators and test statistics. Topics are:

• Optimal and best linear unbiased estimators,
• Cramér-Rao bound in exponential families,
• sufficiency, completeness and the Lehmann-Scheffé theorem,
• the multivariate normal distribution,
• convergence in distribution and multivariate central limit theorem,
• Glivenko-Cantelli theorem,
• limit theorems for U-statistics,
• asymptotic estimation theory (maximum likelihood estimator),
• asymptotic relative efficiency of estimators,
• Neyman-Pearson tests and optimal unbiased tests,
• asymptotic tests in parametric models (likelihood ratio tests).

The contents of the courses "Probability theory" and "Statistics" are strongly recommended.

Total workload: 240 hours

Attendance: 90 hours

• lectures, problem classes, and examination 

Self-studies: 150 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination