# Fundamentals of Mathematical Statistics

Autumn semester 2023

## General information

Lecturer Prof. Sara van de Geer Felix Kuchelmeister, Harald Besdziek Tue 8-10 HG E 3 >> 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 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.