Fundamentals of Mathematical Statistics

Autumn semester 2021

General information

Lecturer Prof. Sara van de Geer
Assistants Felix Kuchelmeister, Harald Besdziek
Lectures Tue 8-10 HG E 5 >>
Wed 10-12 HG E 7 >>
The recordings of the lecture will be available here (it takes some time until they are uploaded).
The lectures can be followed live here.
Exercises Tue 12-13 HG E 7 >> and via Zoom (for the link, see the "Exercises" tab)
Course catalogue data >>

Course content

The course covers the basics of inferential statistics.


  • We provide one exam without solution here.
  • Here is an overview of the topics covered in the exam (same as 2020)
  • The Question Hour takes place on January 21, 2022, 11:00, via Zoom:

Course materials

Lecture notes of the course: Lecture Notes AS 2021. Lecture notes in German of the course taught in 2005 by H.R. Künsch: Lecture Notes AS 2005.


Tentative schedule

Date Topics Chapters
Tue, 21.09.2021 Introduction Chapter 1
Wed, 22.09.2021 Estimation Chapter 2
Tue, 28.09.2021 Likelihood methods Subsection 2.4.3
Wed, 29.09.2021 Intermezzo: distribution theory Chapter 3
Tue, 05.10.2021 Sufficiency and exponential families Chapter 4
Wed, 06.10.2021 Canonical form of an exponential family Section 4.5
Tue, 12.10.2021 Bias, variance and the Cramér Rao lower bound Chapter 5
Wed, 13.10.2021 Completeness for exponential families Section 5.4
Tue, 19.10.2021 Tests and confidence intervals Chapter 6
Wed, 20.10.2021 Equivalence confidence intervals and tests Section 6.3
Tue, 26.10.2021 The Neyman Pearson Lemma and UMP tests Chapter 7
Wed, 27.10.2021 Unbiased tests Section 7.5
Tue, 02.11.2021 Comparison of estimators Chapter 8
Wed, 03.11.2021 Equivariant statistics Chapter 9
Tue, 09.11.2021 Decision theory Chapter 10
Wed, 10.11.2021 Construction of Bayes estimators Section 10.5
Tue, 16.11.2021 Proving admissibility and minimaxity Chapter 11
Wed, 17.11.2021 The linear model Chapter 12
Tue, 23.11.2021 Distribution of the least squares estimator Section 12.3
Wed, 24.11.2021 Asymptotic theory Chapter 13
Tue, 30.11.2021 M-estimators Chapter 14
Wed, 01.12.2021 Asymptotic normality of the MLE Section 14.3
Tue, 07.12.2021 Asymptotic relative efficiency Section 14.6
Wed, 08.12.2021 Likelihood ratio tests Section 14.10
Tue, 14.12.2021 Complexity regularization Chapter 16
Wed, 15.12.2021 The ridge and Lasso penalty Section 16.5
Tue, 21.12.2021 Overview
Wed, 22.12.2021 Buffer

Exercise classes

Exercise classes take place every week, starting on September 28, 2021. The new exercises will be explained, and questions will be answered. Please send your questions in advance per e-mail such that the assistants can prepare.

There will be a question hour shortly before the exam. For details, have a look at the "Announcements" tab.

Series and solutions

We do not correct exercise series. The new exercises and solutions are uploaded on Thursday evenings.