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Information on the lecture Mathematical Statistics (WS 2024/2025)

Lecturer: Dr. Ernst August v. Hammerstein

Assistent: Sebastian Stroppel, M.Sc.

Date: Mon, Wed, 2-4 p.m., SR 404, Ernst-Zermelo-Straße 1

Exercise: 2 hours, date to be determined

ETCS: 9 points

Language: English

 

 

Contents

The lecture builds on basic knowledge about Probability Theory. The fundamental problem of statistics is to infer from a sample of observations as precise as possible statements about the data-generating process or the underlying distributions of the data. For this purpose, the most important methods from statistical decision theory such as test and estimation methods are introduced in the lecture.
Key words hereto include Bayes estimators and tests, Neyman-Pearson test theory, maximum likelihood estimators, UMVU estimators, exponential families, linear models. Other topics include ordering principles for reducing the complexity of models (sufficiency and invariance).
Statistical methods and procedures are used not only in the natural sciences and medicine, but in almost all areas in which data is collected and analyzed This includes, for example, economics (“econometrics”) and the social sciences (especially psychology). However, in the context of this lecture, we will focus less on applications, but—as the name suggests—more on the mathematical justification of the methods.

 

News

  • All course materials (lecture notes and slides, exercise sheets etc.) will be available on the electronic teaching platform ILIAS. To join the ILIAS course, please register for the lecture in HISinOne, you will then automatically be added to the ILIAS course (within one day).

 

Examination (Prüfungsleistung) and pass/fail assessment (Studienleistung)

To obtain the ECTS points for this course, you have to succeed in the pass/fail assessment and---depending on your course of studies and the module you choose for this course---also pass an oral examination.
For the former, you should earn at least 50% of the maximally accessible exercise points and additionally present one solution of an exercise in the tutorial.

 

Tutorial and exercise sheets

The lecture will be accompanied by a weekly tutorial in which solutions to the exercise sheets will be discussed and further questions concerning specific lecture contents can be answered. Currently, there are two possible dates at which the tutorial can take place:
        Tuesdays from 16-18 in SR 127/128, Ernst-Zermelo-Str. 1
or    Thursdays from 16-18 in SR 127/128, Ernst-Zermelo-Str. 1.
The exact date will be fixed together with all participants in the first lecture on October 14, 2024.

Depending on which day the tutorial will take place, the weekly exercise sheets will be uploaded on ILIAS on Mondays or Wednesdays after the lecture. You should submit your solutions until the same day in the subsequent week, either in paper form in the designated letterbox in the basement of the math building Ernst-Zermelo-Str. 1 or by uploading them in digital form on ILIAS.

 

Literature

 

Necessary prior knowledge

Probability Theory (in particular measure theory and conditional probabilities/expectations)

 

Usable in the following modules:

Compulsory elective module Mathematics (BSc21)
Applied Mathematics, Mathematics or (in agreement with the examiner) Concentration Module (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)
Mathematical Concentration (MEd18, MEH21)
Elective (MSc14)
Elective for individual studying (2HfB21)

 

Consultation Hours

Lecturer consultation hours: Thursdays 10-11 a.m.
For shorter questions, you can also send an email to
Assistent consultation hours: by appointment