Fundamentals of Mathematical Statistics
Autumn semester 2023
General information
| Lecturer | Prof. Sara van de Geer |
|---|---|
| Assistants | Felix Kuchelmeister, Harald Besdziek |
| Lectures | Tue 8-10 HG E 3 >> |
| Wed 10-12 HG E 7 >> | |
| Exercises | Tue 12-13 HG E 7 >> |
| Course catalogue data | >> |
Course content
The course covers the basics of inferential statistics.
Announcements
- We provide one old exam here: Exam / Formulae sheet / Solution
- Here is an overview of the topics covered in the exam.
- Doctoral students from D-MATH who want to get credits need to submit 6/11 solved exercises via email.
Course materials
Lecture notes of the course: Lecture Notes AS 2023.
The recordings from AS 2021 may be found at the video portal (the content should be similar to this year).
Lecture notes in German of the course taught in 2005 by H.R. Künsch: Lecture Notes AS 2005.Tentative schedule
| Date | Topics | Chapters |
|---|---|---|
| Tue, 19.09.2023 | Introduction | Chapter 1 |
| Wed, 20.09.2023 | Estimation | Chapter 2 |
| Tue, 26.09.2023 | Likelihood methods | Subsection 2.4.3 |
| Wed, 27.09.2023 | Intermezzo: distribution theory | Chapter 3 |
| Tue, 03.10.2023 | Sufficiency and exponential families | Chapter 4 |
| Wed, 04.10.2023 | Canonical form of an exponential family | Section 4.5 |
| Tue, 10.10.2023 | Bias, variance and the Cramér Rao lower bound | Chapter 5 |
| Wed, 11.10.2023 | Completeness for exponential families | Section 5.4 |
| Tue, 17.10.2023 | Tests and confidence intervals | Chapter 6 |
| Wed, 18.10.2023 | Equivalence confidence intervals and tests | Section 6.3 |
| Tue, 24.10.2023 | The Neyman Pearson Lemma and UMP tests | Chapter 7 |
| Wed, 25.10.2023 | Unbiased tests | Section 7.5 |
| Tue, 31.10.2023 | Comparison of estimators | Chapter 8 |
| Wed, 01.10.2023 | Equivariant statistics | Chapter 9 |
| Tue, 07.11.2023 | Decision theory | Chapter 10 |
| Wed, 08.11.2023 | Construction of Bayes estimators | Section 10.5 |
| Tue, 14.11.2023 | Proving admissibility and minimaxity | Chapter 11 |
| Wed, 15.11.2023 | The linear model | Chapter 12 |
| Tue, 21.11.2023 | Distribution of the least squares estimator | Section 12.3 |
| Wed, 22.11.2023 | Asymptotic theory | Chapter 13 |
| Tue, 28.11.2023 | M-estimators | Chapter 14 |
| Wed, 29.11.2023 | Asymptotic normality of the MLE | Section 14.3 |
| Tue, 05.12.2023 | Asymptotic relative efficiency | Section 14.6 |
| Wed, 06.12.2023 | Likelihood ratio tests | Section 14.10 |
| Tue, 12.12.2023 | Complexity regularization | Chapter 16 |
| Wed, 13.12.2023 | The ridge and Lasso penalty | Section 16.5 |
| Tue, 19.12.2023 | Overview | |
| Wed, 20.12.2023 | Buffer |
Exercise classes
Exercise classes take place every week in HG E 7, starting on September 26, 2023. 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.
Series and solutions
We do not correct exercise series.