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.
Announcements
- 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: https://ethz.zoom.us/j/64582046830
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.Slides
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.