Statistical Decision Theory / Asymptotic Mathematical Theory of Statistics

Lecture in Winter term 2026 / 2027

Organization

Lecturers: Prof. Dr. Enno Mammen
Teaching assistants: Klaus Stier

Lecture schedule

Lecture content

This is a course in Mathematical Statistics that is split into two halfs.

1. Statistical Decision Theory
2. Asymptotic Mathematical Theory of Statistics

Organization of the Course

The lecture time slots are on TBA. The tutorials take place biweekly on TBA. Please sign up for this lecture on MaMpf as well!
The lecture partially follows the flipped classroom model.

Lecture

The topic of the current week is presented by the lecturer. Participants should work through the details using the lecture notes. New exercises related to the topic of the week are presented and briefly discussed. The exercises can be found in the lecture notes.
Questions about last week's material will be covered.
One exercise from last weeks exercises will be discussed.

Tutotrials (biweekly)

The remaining exercises of last week are discussed. Moreover, it is discussed which details from the lecture notes of the current week shall be discussed in the following lecture. It is also possible to (always) send your wishes for the next session via email until Friday noon to the assistant.

Deviations in the first week (applies to both parts)

During the first lecture, only the content of the first week is presented. The first exercises will be shortly discussed. Naturally, (2) and (3) from above are omitted.
In addition the concept of the lecture will be discussed. If there are suggestions for changes in the concept, we can discuss these as well.

Detailed Overview of the Topics

This is a master level course in Mathematical Statistics that is split into two halfs.

1. Statistical Decision Theory

(Week 1) Introduction to testing theory, Neyman-Pearson-Lemma
(Week 2) Generalized Neyman-Pearson Lemma; Statistical decision problems; Sufficient Statistics; Neymans Factorization criterion
(Week 3) Prof of Theorem 2.7; Rao-Blackwell Theorem; Exponential Families
(Week 4) Conditional Optimal Tests I
(Week 5) Conditional Optimal Tests II
(Week 6) Examples
(Week 7) Exam for the first half of the course

2. Asymptotic Mathematical Theory of Statistics
This part is also organised in seven weeks, starting the week after the exam of the first half.

(Week 1) Introduction; Extremum estimators: some examples; Consistency of extremum estimators
(Week 2) Asymptotic normality of extremum estimators; Testing procedures based on extremum estimators
(Week 3) ML-estimators, differentiability in quadratic mean (DQM)
(Week 4) Local Asymptotic Normality (LAN); LeCam Theory
(Week 5) Power of rank tests; Power of Wald test; Contiguity; Optimality theory in LAN experiments
(Week 6) ML-estimation in DQM families
(Week 7) Exam for the second half of the course

Exercise groups

At this time, there is no teaching assistant available for the course, so there will be no graded assignments. Should this situation change, you will be notified promptly.

Exercises

A collection of relevant exercises is included in the lecture notes. Each week, we will recommend some specific exercises to work on. Some of these recommended exercises will be covered in the lecture the following week, while the others will be covered in the biweekly tutorials.

Exam

The two content sections (see course content) will be examined separately. The exam for Part 1 is expected to take place in late November, the exam for Part 2 at the end of the lecture period.

Final Grade

The final grade is given by the average of the two grades from the exam. The final grade will be rounded up in your favor.