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Modul
Mathematical Statistics [M-MATH-102909]
Credits
8Recurrence
Jedes WintersemesterDuration
1 SemesterLanguage
Level
4Version
2Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-105872 | Mathematical Statistics | 8 |
Competence Certificate
The module will be completed by an oral exam (approx. 30 min).
Competence Goal
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.
Prerequisites
none
Content
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).
Recommendation
The contents of the courses "Probability theory" and "Statistics" are strongly recommended.
Workload
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