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Institut für Stochastik

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 2.056 und 2.002

Adresse
Karlsruher Institut für Technologie
Institut für Stochastik

Englerstr. 2
D-76131 Karlsruhe

Postadresse:
D-76128 Karlsruhe

Öffnungszeiten:
Mo-Fr 10:00 - 12:00

Tel.: 0721 608 43270/43265

Fax.: 0721 608 46066

Asymptotic Stochastics (Wintersemester 2013/14)

Dozent: Prof. 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
Dozenten
Dozent Prof. 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.