# Fundamentals of Mathematical Statistics

Autumn semester 2019

## General information

Lecturer Prof. Sara van de Geer Jeffrey Näf, Francesco Ortelli Tue 8-10 HG E 5 >> Wed 10-12 HG F 3 >> Tue 12-13 HG E 5 >> >>

## Course content

The course covers the basics of inferential statistics.

## Announcements

• 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.