Fundamentals of Mathematical Statistics
Autumn semester 2018
General information
| Lecturer | Prof. Sara van de Geer |
|---|---|
| Assistants | Jeffrey Näf, Peter Hinz |
| Lectures | Wed 10-12 and Tue 8-10 HG E 1.1 >> |
| Exercises | Tue 12-13 HG E 1.1 >> |
| Course catalogue data | >> |
Course content
The course covers the basics of inferential statistics.
Announcements
-
August 19, 2018:
Beginning of lecture: Tuesday, 18/09/2018. -
August 19, 2018:
First exercise class: Tuesday, 25/09/2018. -
November 05, 2018:
Question hour in HG G19.1: Tuesday, 13/11/2018 17:00-18:00. -
December 07, 2018:
Question hour in HG G19.1: Friday, 18/01/2019 15:00-16:00. -
December 07, 2018:
Question hour in HG G19.2: Tuesday, 22/01/2019 16:00-17:00. -
December 07, 2018:
Exam consultation in HG G19.1: Thursday, 28/02/2019 12:00-13:00.
Course materials
Lecture notes of the course: Lecture Notes AS 2018.Overview of the course content. Old exam.
Lecture notes in German of the course taught in 2005 by H.R. Künsch: Lecture Notes AS 2005 .
Tentative schedule
| Date | Topics | Chapters |
|---|---|---|
| Tue, 18.9.2018 | Introduction | Chapter 1 |
| Wed, 19.09.2018 | Estimation | Chapter 2 |
| Tue, 25.09.2018 | Likelihood methods | Subsection 2.4.3 |
| Wed, 26.09.2018 | Intermezzo: distribution theory | Chapter 3 |
| Tue, 2.10.2018 | Sufficiency and exponential families | Chapter 4 |
| Wed, 3.10.2018 | Canonical form of an exponential family | Section 4.5 |
| Tue, 9.10.2018 | Bias, variance and the Cramér Rao lower bound | Chapter 5 |
| Wed, 10.10.2018 | Completeness for exponential families | Section 5.4 |
| Tue, 16.10.2018 | Tests and confidence intervals | Chapter 6 |
| Wed, 17.10.2018 | Equivalence confidence intervals and tests | Section 6.3 |
| Tue, 23.10.2018 | The Neyman Pearson Lemma and UMP tests | Chapter 7 |
| Wed, 24.10.2018 | Unbiased tests | Section 7.5 |
| Tue, 30.10.2018 | Comparison of estimators | Chapter 8 |
| Wed, 31.10.2018 | Equivariant statistics | Chapter 9 |
| Tue, 6.11.2018 | Decision theory | Chapter 10 |
| Wed, 7.11.2018 | Construction of Bayes estimators | Section 10.5 |
| Tue, 13.11.2018 | Proving admissibility and minimaxity | Chapter 11 |
| Wed, 14.11.2018 | The linear model | Chapter 12 |
| Tue, 20.11.2018 | Distribution of the least squares estimator | Section 12.3 |
| Wed, 21.11.2018 | Asymptotic theory | Chapter 13 |
| Tue, 27.11.2018 | M-estimators | Chapter 14 |
| Wed, 28.11.2018 | Asymptotic normality of the MLE | Section 14.3 |
| Tue, 4.11.2018 | Asymptotic relative efficiency | Section 14.6 |
| Wed, 5.12.2018 | Likelihood ratio tests | Section 14.10 |
| Tue, 11.12.2018 | Complexity regularization | Chapter 16 |
| Wed, 12.12.2018 | The ridge and Lasso penalty | Section 16.5 |
| Tue, 18.12.2018 | Overview | |
| Wed, 19.12.2018 | Buffer |