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 video.ethz.ch (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.
Announcements
- 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 here.
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).