Asymptotic Stochastics (Wintersemester 2013/14)
- Dozent*in: Prof. i. R. Dr. Norbert Henze
- Veranstaltungen: Vorlesung (0118000), Übung (0118100)
- Semesterwochenstunden: 4+2
| Termine | |||
|---|---|---|---|
| Vorlesung: | Dienstag 11:30-13:00 | Z 1 | Beginn: 22.10.2013 |
| Donnerstag 11:30-13:00 | Z 1 | ||
| Übung: | Montag 14:00-15:30 | Z 1 | Beginn: 28.10.2013 |
| Lehrende | ||
|---|---|---|
| Dozent | Prof. i. R. Dr. Norbert Henze | |
| Sprechstunde: nach Vereinbarung | ||
| Zimmer 2.020, Sekretariat 2.002 Kollegiengebäude Mathematik (20.30) | ||
| Email: henze@kit.edu | Übungsleiterin | Dr. Viola Riess |
| Sprechstunde: | ||
| Zimmer Allianz-Gebäude (05.20) | ||
| Email: viola.riess@kit.edu | ||
Inhalt
- Convergence in distribution,
- method of moments,
- multivariate normal distribution,
- characteristic functions and convergence in distribution in R^d,
- delta method,
- a Poisson limit theorem for triangular arrays,
- Central limit theorem for m-dependent stationary sequences,
- Glivenko-Cantelli’s theorem,
- limit theorems for U-statistics,
- asymptotic properties of maximum likelihood and moment estimators,
- asymptotic optimality of estimators,
- asymptotic confidence regions,
- likelihood ratio tests,
- weak convergence in metric spaces,
- Brown Wiener Process,
- Donsker’s theorem,
- Brownian bridge,
- goodness-of-fit tests
Voraussetzungen
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 und Aktuelles
Course Material and important information can be found here (Studierendenportal)
Prüfung
There will be oral examinations on the following dates:
Friday, February 28th 2014
Thursday, April 10th 2014
Friday, April 11th 2014
For information about registration (procedure, deadlines,...) please visit the course page (Studierendenportal) or contact Ms. Riess.
Literaturhinweise
- Billingsley, P. (1986): Probability and Measure. Wiley, New York.
- Billingsley, P. (1968): Convergence of probability measures. Wiley, New York.
- Durrett, R. (2010): Probability Theory. Theory and Examples. Fourth Edition. Cambridge University Press.
- 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.
- Shao, J. (2003): Mathematical Statistics. Second edition. Springer, New York.