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Applied Stochastics

Statistical Analysis (Mathematical Statistics)

08043700 · Statistical Analysis (Mathematical Statistics)

Lecturer: Prof. Dr. Markus Bibinger

Tutor: Michael Sonntag

  • Date and location:  Wednesday 4-6 pm Note: There will be asynchronous lectures provided online. The synchronous lecture on Wednesday is either at Helmut-Pabel-Hörsaal and hybrid or via zoom. This is determined later depending on the pandemic situation.
  • Start: October 20, 2021, 4:15 pm
  • Exercises (Vst.-Nr.  08043750): ... Note: the lecture will be online.
  • Exam WS 2021/2022: Oral exams,  appointments are assigned later.
  • Registration for the exam WS 2021/2022: Via WueStudy, registration period will be announced during the lecture.
  • Language: English (or German). Please contact us if you want to participate and if you have constraints.

Contents of the lecture:

This lecture gives an introduction to mathematical statistics. Key topics are hypothesis testing and point estimation. We shall discuss asymptotic statistics, concepts of optimality and information theory with dimensionality reduction and sufficiency. In particular, the lecture contains the following contents:

  • Statistical models, point estimation, hypothesis testing and confidence
  • Statistics for the linear model
  • Decision theory, minimax and Bayes optimality, admissibility and the Stein phenomenon
  • Exponential families, sufficiency and completeness of statistics
  • Asymptotic theory for point estimators
  • Neyman-Pearson test theory, UMP and UMPU tests

Requirements: Introduction to probability with measure theory


  • Lehmann, E.L.: Testing Statistical Hypotheses, Springer, 1997
  • Lehmann, E.L. and G. Casella: Theory of Point Estimation, Springer, 2003
  • Shao, J.: Mathematical Statistics, Springer, 2003
  • Wasserman, L.: All of Statistics, Springer, 2003
  • Witting, H.: Mathematische Statistik I, Teubner, 1985



(1) Registration (Vst.-Nr. 08043750) in WueStudy is required.

(2) Materials (lecture notes, videos, exercise sheets) via WueCampus (Link)