Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-62-11-K-7

Mathematical Statistics (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Livecycle-State [NORM] Active

Contents

  • Asymptotic analysis of M-estimators, especially of Maximum-Likelihood-estimators,
  • Bayes-and Minimax-estimators,
  • Likelihood-ratio-tests: asymptotic analysis and examples (t-test, c²-goodness-of-fit-test)
  • Glivenko-Cantelli-theorem, Kolmogorov-Smirnov-test,
  • Differentiable statistic functionals and examples of applications (derivation of asymptotic results, robustness),
  • Resampling methods on the basis of Bootstraps.

Literature

  • G. Casella, R. Berger: Statistical Inference,
  • L. Breiman: Statistics,
  • P. Bickel, K. Doksum: Mathematical Statistics,
  • R. Serfling: Approximation Theorems of Mathematical Statistics,
  • J. Shao: Mathematical Statistics.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-62-11-K-7]

Module Name Context
[MAT-62-11-M-7] Mathematical Statistics P: Obligatory 4V+2U, 9.0 LP