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Institute of Stochastics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.056 und 2.002

Address
Karlsruher Institut für Technologie
Institut für Stochastik

Englerstr. 2
D-76131 Karlsruhe

Postadresse:
D-76128 Karlsruhe

Office hours:
Mo-Fr 10:00 - 12:00

Tel.: +49 721 608 43270/43265

Fax.: +49 721 608 46066

Asymptotic Stochastics (Winter Semester 2013/14)

Lecturer: Prof. Dr. Norbert Henze
Classes: Lecture (0118000), Problem class (0118100)
Weekly hours: 4+2


Schedule
Lecture: Tuesday 11:30-13:00 Z 1 Begin: 22.10.2013
Thursday 11:30-13:00 Z 1
Problem class: Monday 14:00-15:30 Z 1 Begin: 28.10.2013
Lecturers
Lecturer Prof. Dr. Norbert Henze
Office hours: On appointment.
Room 2.020, Sekretariat 2.002 Kollegiengebäude Mathematik (20.30)
Email: henze@kit.edu
Problem classes Dr. Viola Riess
Office hours:
Room Allianz-Gebäude (05.20)
Email: viola.riess@kit.edu

Contents

  • 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

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 and Information

Course Material and important information can be found here (Studierendenportal)

Examination

There will be oral examinations. Dates will be annouced towards the end of the semester.

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.

References

  • 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.