Fundamentals of Mathematical Statistics

Autumn semester 2020

General information

Lecturer Prof. Sara van de Geer
Assistants Jeffrey Näf, Peter Hinz
Lectures online Recorded every Tue 8-10, Wed 10-12
Available with a delay at (not zoom)
Live lecture here
Exercises Tue 12-13 via zoom, link on "exercise" tab.
Course catalogue data >>

Course content

The course covers the basics of inferential statistics.


  • We published the zoom details for the exercises on the "Exercises" tab
  • We provide one exam without solution here.

Course materials

Lecture notes of the course: Lecture Notes AS 2020.
Slides Please note that on slide CH5, p.18 there is a "h" missing, the lecture notes p.51 list the correct CRLB condition II.
Lecture notes in German of the course taught in 2005 by H.R. Künsch: Lecture Notes AS 2005
Lecture recordings will be available one day after the corresponding lecture

Tentative schedule

Date Topics Chapters
Tue, 15.9.2020 Introduction Chapter 1
Wed, 16.09.2020 Estimation Chapter 2
Tue, 22.09.2020 Likelihood methods Subsection 2.4.3
Wed, 23.09.2020 Intermezzo: distribution theory Chapter 3
Tue, 29.9.2020 Sufficiency and exponential families Chapter 4
Wed, 30.9.2020 Canonical form of an exponential family Section 4.5
Tue, 6.10.2020 Bias, variance and the Cramér Rao lower bound Chapter 5
Wed, 7.10.2020 Completeness for exponential families Section 5.4
Tue, 13.10.2020 Tests and confidence intervals Chapter 6
Wed, 14.10.2020 Equivalence confidence intervals and tests Section 6.3
Tue, 20.10.2020 The Neyman Pearson Lemma and UMP tests Chapter 7
Wed, 21.10.2020 Unbiased tests Section 7.5
Tue, 27.10.2020 Comparison of estimators Chapter 8
Wed, 28.10.2020 Equivariant statistics Chapter 9
Tue, 3.11.2020 Decision theory Chapter 10
Wed, 4.11.2020 Construction of Bayes estimators Section 10.5
Tue, 10.11.2020 Proving admissibility and minimaxity Chapter 11
Wed, 11.11.2020 The linear model Chapter 12
Tue, 17.11.2020 Distribution of the least squares estimator Section 12.3
Wed, 18.11.2020 Asymptotic theory Chapter 13
Tue, 24.11.2020 M-estimators Chapter 14
Wed, 25.11.2020 Asymptotic normality of the MLE Section 14.3
Tue, 1.12.2020 Asymptotic relative efficiency Section 14.6
Wed, 2.12.2020 Likelihood ratio tests Section 14.10
Tue, 8.12.2020 Complexity regularization Chapter 16
Wed, 9.12.2020 The ridge and Lasso penalty Section 16.5
Tue, 15.12.2020 Overview
Wed, 16.12.2020 Buffer

Exercise classes

Exercise classes are every week starting on September 22, 2020 via zoom. The new exercises will be explained and questions are answered. Please send your questions in advance per mail such that the assistants can prepare.

For the zoom details, please see below.

Series and solutions

We do not correct exercise series. Only exception: PhD students who need ETH credit points.

PhD students who only need the ETH credit points have to hand in solutions to at least 8 problem sheets via email until one week after the prelimiary discussion of the respective exercise series. PhD students who need ECTS points do not have to hand in solutions but have to pass the exam (an online registration on mystudies is required).