# Fundamentals of Mathematical Statistics

Autumn semester 2022

## General information

Lecturer Prof. Sara van de Geer Jeffrey Näf, Harald Besdziek Tue 8-10 HG E 5 >> Wed 10-12 HG E 7 >> Tue 12-13 HG E 7 >> >>

## Course content

The course covers the basics of inferential statistics.

## Announcements

• We provide one exam without solution here.
• Here is an overview of the topics covered in the exam.

## Course materials

Lecture notes of the course: Lecture Notes AS 2022.

The recordings from last year 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, 20.09.2022 Introduction Chapter 1
Wed, 21.09.2022 Estimation Chapter 2
Tue, 27.09.2022 Likelihood methods Subsection 2.4.3
Wed, 28.09.2022 Intermezzo: distribution theory Chapter 3
Tue, 04.10.2022 Sufficiency and exponential families Chapter 4
Wed, 05.10.2022 Canonical form of an exponential family Section 4.5
Tue, 11.10.2022 Bias, variance and the Cramér Rao lower bound Chapter 5
Wed, 12.10.2022 Completeness for exponential families Section 5.4
Tue, 18.10.2022 Tests and confidence intervals Chapter 6
Wed, 19.10.2022 Equivalence confidence intervals and tests Section 6.3
Tue, 25.10.2022 The Neyman Pearson Lemma and UMP tests Chapter 7
Wed, 26.10.2022 Unbiased tests Section 7.5
Tue, 01.11.2022 Comparison of estimators Chapter 8
Wed, 02.11.2022 Equivariant statistics Chapter 9
Tue, 08.11.2022 Decision theory Chapter 10
Wed, 09.11.2022 Construction of Bayes estimators Section 10.5
Tue, 15.11.2022 Proving admissibility and minimaxity Chapter 11
Wed, 16.11.2022 The linear model Chapter 12
Tue, 22.11.2022 Distribution of the least squares estimator Section 12.3
Wed, 23.11.2022 Asymptotic theory Chapter 13
Tue, 29.11.2022 M-estimators Chapter 14
Wed, 30.11.2022 Asymptotic normality of the MLE Section 14.3
Tue, 06.12.2022 Asymptotic relative efficiency Section 14.6
Wed, 07.12.2022 Likelihood ratio tests Section 14.10
Tue, 13.12.2022 Complexity regularization Chapter 16
Wed, 14.12.2022 The ridge and Lasso penalty Section 16.5
Tue, 20.12.2022 Overview
Wed, 21.12.2022 Buffer

## Exercise classes

Exercise classes take place every week, starting on September 27, 2022. 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.

Exercises Solutions