Fundamentals of Mathematical Statistics
Autumn semester 2017
General information
| Lecturer | Prof. Sara van de Geer |
|---|---|
| Assistants | Andreas Elsener, Gian Thanei, Peter Hinz |
| Lectures | Wed 10-12 and Fri 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 22, 2017:
Beginning of lecture: Wednesday, 20/09/2017. -
August 22, 2017:
First exercise class: Tuesday, 26/09/2017.
Course materials
Lecture notes of the course taught in 2015: Lecture Notes AS 2015.An updated version of the lecture notes will be posted at the beginning of the semester: Lecture Notes AS 2017.
Lecture notes in German of the course taught in 2005 by H.R. Künsch: Lecture Notes AS 2005 .
Tentative schedule
| Date | Topics | Chapters |
|---|---|---|
| Wed, 20.09.2017 | Introduction | Chapter 1 |
| Fri, 22.09.2017 | Estimation | Chapter 2 |
| Wed, 27.09.2017 | Likelihood methods | Subsection 2.4.3 |
| Fri, 29.09.2017 | Intermezzo: distribution theory | Chapter 3 |
| Wed, 4.10.2017 | Sufficiency and exponential families | Chapter 4 |
| Fri, 6.10.2017 | Canonical form of an exponential family | Section 4.5 |
| Wed, 11.10.2017 | Bias, variance and the Cramér Rao lower bound | Chapter 5 |
| Fri, 13.10.2017 | Completeness for exponential families | Section 5.4 |
| Wed, 18.10.2017 | Tests and confidence intervals | Chapter 6 |
| Fri, 20.10.2017 | Equivalence confidence intervals and tests | Section 6.3 |
| Wed, 25.10.2017 | The Neyman Pearson Lemma and UMP tests | Chapter 7 |
| Fri, 27.10.2017 | Unbiased tests | Section 7.5 |
| Wed, 1.11.2017 | Comparison of estimators | Chapter 8 |
| Fri, 3.11.2017 | Equivariant statistics | Chapter 9 |
| Wed, 8.11.2017 | Decision theory | Chapter 10 |
| Fri, 10.11.2017 | Construction of Bayes estimators | Section 10.5 |
| Wed, 15.11.2017 | Proving admissibility and minimaxity | Chapter 11 |
| Fri, 17.11.2017 | The linear model | Chapter 12 |
| Wed, 22.11.2017 | Distribution of the least squares estimator | Section 12.3 |
| Fri, 24.11.2017 | Asymptotic theory | Chapter 13 |
| Wed, 29.11.2017 | M-estimators | Chapter 14 |
| Fri, 1.12.2017 | Asymptotic normality of the MLE | Section 14.3 |
| Wed, 6.12.2017 | Asymptotic relative efficiency | Section 14.6 |
| Fri, 8.12.2017 | Likelihood ratio tests | Section 14.10 |
| Wed, 13.12.2017 | Complexity regularization | Chapter 16 |
| Fri, 15.12.2017 | The ridge and Lasso penalty | Section 16.5 |
| Wed, 20.12.2017 | Overview | |
| Fri, 22.12.2017 | Buffer |
Exercise classes
Exercise classes are every week starting on September 26, 2017.
Series and solutions
The Series solutions 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.
PhD Students who only need the ETH credit points have to hand in solutions to at least 8 problem sheets. If you need ECTS points, you do not have to hand in solutions but to pass the exam (an online registration on mystudies is required).
| Exercises | Solutions | Due date |
|---|---|---|
| Series 1 | Solutions 1 | October 3, 2017 |
| Series 2 | Solutions 2 (fixed typo 17.10.) | October 10, 2017 |
| Series 3 | Solutions 3 | October 17, 2017 |
| Series 4 | Solutions 4 | October 24, 2017 |
| Series 5, Hints | Solutions 5 (extended solution for ex3) | October 31, 2017 |
| Series 6 | Solutions 6 | November 7, 2017 |
| Series 7 | Solutions 7 | November 14, 2017 |
| Series 8 | Solutions 8 | November 21, 2017 |
| Series 9 (corrected typo in ex2) | Solutions 9 | November 28, 2017 |
| Series 10 | Solutions 10 | December 5, 2017 |
| Series 11 | Solutions 11 | December 12, 2017 |
| Series 12 | Solutions 12 | December 19, 2017 |