Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-62-11-M-7

Mathematical Statistics (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-62-11-M-7 Mathematical Statistics 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-62-11-K-7
Mathematical Statistics
P 84 h 186 h - - PL1 9.0 WiSe
  • About [MAT-62-11-K-7]: Title: "Mathematical Statistics"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86300 ("Mathematical Statistics")

Evaluation of grades

The grade of the module examination is also the module grade.


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.

Competencies / intended learning achievements

Upon successful completion of the moule the students know and understand classical and modern asymptotic approaches and techniques of proofs for mathematical statistics as well as their usability to solve practical relevant problems. They are able to apply methods of mathematical statistics by themselves.

By completing the exercises, students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the course. They understand the proofs presented in the lecture and are able to reproduce and explain them. They can in particular outline the conditions and assumptions that are necessary for the validity of the statements.

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.

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 Module / Module Number [MAT-62-11-M-7]

Course of Study Section Choice/Obligation
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Statistics and Computational Methods [WP] Compulsory Elective
Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)