Asymptotic Stochastics (Winter Semester 2015/16)
- Lecturer: Prof. Dr. Vicky Fasen-Hartmann
- Classes: Lecture (0118000), Problem class (0118100)
- Weekly hours: 4+2
Aktuelles
Die Vorlesung am Donnerstag, 17. 12. 2015, muss wegen Krankheit leider kurzfristig entfallen.
| Schedule | ||
|---|---|---|
| Lecture: | Wednesday 8:00-9:30 | SR 0.014 |
| Thursday 11:30-13:00 | SR 0.014 | |
| Problem class: | Friday 9:45-11:15 | SR 0.014 |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Dr. Vicky Fasen-Hartmann | |
| Office hours: On appointment. | ||
| Room 2.053 Kollegiengebäude Mathematik (20.30) | ||
| Email: vicky.fasen@kit.edu | Problem classes | Dr. Sebastian Kimmig |
| Office hours: Mittwoch 14:00 - 15:00 Uhr und nach Vereinbarung | ||
| Room 2.011 Kollegiengebäude Mathematik (20.30) | ||
| Email: sebastian.kimmig@kit.edu | ||
Content
- Basic facts from probability theory
- Convergence in R^d (the multivariate normal distribution, Convergence in distribution,CLT in R^d)
- Empirical distribution functions
- A CLT for m-dependent stationary sequences
- Estimation theory (Asymptotic properties of maximum likelihood estimators,Asymptotic (relative) efficiency of estimators, Likelihood ratio test)
- U-statistics
- Probability measures on metric spaces (weak convergence in metric spaces, relative compactness and tightness, weak convergence and tightness in C)
- Donsker's theorem
- Empirical processes: applications in statistics.
Prerequisites
A sound working knowledge in measure-theory based on probability theory
(especially strong law of large numbers, convergence in distribution in R^1, Central limit
theorem of Lindeberg-Lévy), and statistical concepts (tests, confidence regions).
Material
Course Material and important information can be found in the ILIAS course of the lecture.
Examination
There will be oral examinations towards the end of the semester. All further details can be found in the ILIAS course of the lecture.
References
- Billingsley, P. (1986): Probability and Measure. Wiley, New York.
- Billingsley, P. (1968): Convergence of probability measures. Wiley, New York.
- Ferguson, Th.S. (1996): A Course in Large Sample Theory. Chapman & Hall, London.
- Lee, A.J. (1990): U-Statistics. Theory and practice. Marcel Dekker, New York, Basel.
- Lehmann, E.L. (1999): Elements of large sample theory. Springer, New York.
- Shao, J. (2003): Mathematical Statistics. Second edition. Springer, New York.