Fundamentals of Mathematical Statistics
Autumn semester 2019
General information
| Lecturer | Prof. Sara van de Geer |
|---|---|
| Assistants | Jeffrey Näf, Francesco Ortelli |
| Lectures | Tue 8-10 HG E 5 >> |
| Wed 10-12 HG F 3 >> | |
| Exercises | Tue 12-13 HG E 5 >> |
| Course catalogue data | >> |
Course content
The course covers the basics of inferential statistics.
Announcements
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Question hour 1:
Thursday, 14.11.2019, 16-17, HG E 5.
Send your questions here until Thursday, 07.11.2019 -
Question hour 2:
Tuesday, 17.12.2019, 12-13, HG E 5.
Send your questions here until Tuesday, 10.12.2019 -
Overview
In this document you find an overview over the relevant topics for the examination (Prüfungsstoff). In the exam, the densities and the moments of the relevant distributions will typically be given. The use of pocket calculators or individual written aids at the exam is not allowed.
Course materials
Lecture notes of the course: Lecture Notes AS 2019.Overview of the course content.
Lecture notes in German of the course taught in 2005 by H.R. Künsch: Lecture Notes AS 2005 .
Tentative schedule
| Date | Topics | Chapters |
|---|---|---|
| Tue, 17.9.2019 | Introduction | Chapter 1 |
| Wed, 18.09.2019 | Estimation | Chapter 2 |
| Tue, 24.09.2019 | Likelihood methods | Subsection 2.4.3 |
| Wed, 25.09.2019 | Intermezzo: distribution theory | Chapter 3 |
| Tue, 1.10.2019 | Sufficiency and exponential families | Chapter 4 |
| Wed, 2.10.2019 | Canonical form of an exponential family | Section 4.5 |
| Tue, 8.10.2019 | Bias, variance and the Cramér Rao lower bound | Chapter 5 |
| Wed, 9.10.2019 | Completeness for exponential families | Section 5.4 |
| Tue, 15.10.2019 | Tests and confidence intervals | Chapter 6 |
| Wed, 16.10.2019 | Equivalence confidence intervals and tests | Section 6.3 |
| Tue, 22.10.2019 | The Neyman Pearson Lemma and UMP tests | Chapter 7 |
| Wed, 23.10.2019 | Unbiased tests | Section 7.5 |
| Tue, 29.10.2019 | Comparison of estimators | Chapter 8 |
| Wed, 30.10.2019 | Equivariant statistics | Chapter 9 |
| Tue, 5.11.2019 | Decision theory | Chapter 10 |
| Wed, 6.11.2019 | Construction of Bayes estimators | Section 10.5 |
| Tue, 12.11.2019 | Proving admissibility and minimaxity | Chapter 11 |
| Wed, 13.11.2019 | The linear model | Chapter 12 |
| Tue, 19.11.2019 | Distribution of the least squares estimator | Section 12.3 |
| Wed, 20.11.2019 | Asymptotic theory | Chapter 13 |
| Tue, 26.11.2019 | M-estimators | Chapter 14 |
| Wed, 27.11.2019 | Asymptotic normality of the MLE | Section 14.3 |
| Tue, 3.11.2019 | Asymptotic relative efficiency | Section 14.6 |
| Wed, 4.12.2019 | Likelihood ratio tests | Section 14.10 |
| Tue, 10.12.2019 | Complexity regularization | Chapter 16 |
| Wed, 11.12.2019 | The ridge and Lasso penalty | Section 16.5 |
| Tue, 17.12.2019 | Overview | |
| Wed, 18.12.2019 | Buffer |
Exercise classes
Exercise classes are every week starting on September 24, 2019.
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. 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).
The solved exercise sheet should be handed in by 12.15PM of the designated date. You can submit your solutions to the assistants during the exercise class or by placing them in the Fundamentals of Mathematical Statistics box in room HG J 68.
Submitted solutions that were not recollected will be placed in HG J 68.