Lecture
Statistical Decision Theory / Asymptotic Mathematical Theory of Statistics
Winter term 2025/2026
Links: MUESLI;
heiCO.
Place and Date
- Lecture: Monday 14 - 18h, Place: SR ? (Mathematikon, INF 205)
The first lecture takes place on Monday, October 13.
- Exercise classes: Wednesday 14 - 16h, Place: SR ? (Mathematikon, INF 205)
The first exercise class takes place on Wednesday, October 15.
Hand-in of exercise sheets: on Fridays at 12h. Please hand in your solutions on paper in box no. ?? in the 1st floor of the Mathematikon.
- Exam: Wednesday, November 26 (Part 1) resp. Wednesday, February 4 (Part 2).
Topics
This is a master level course in Mathematical Statistics that is split into two halfs.
- 1. Statistical Decision Theory
- 2. Asymptotic Mathematical Theory of Statistics
A detailed overview of can be found further below.
Organization of the course
The lecture time slots are on Mondays, 14-18h. The tutorials take place on Wednesdays 16-18h. The tutorials are held on Wednesdays by the tutor. The Monday sessions are held by the lecturer.
- Monday 14h - 18h
- The topic of the current week is presented by the lecturer. Participants should work through the details using the script. New exercises related to the topic of the week are presented and briefly discussed.
The exercises can be found in the script.
- Questions about last week's material will be covered.
- One exercise from last week's exercises will be discussed.
- Wednesday 14h - 16h
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 Monday session. It is also possible to send your wishes for the next Monday session via email until Friday 12h to the tutor.
- Friday 12h
Hand-in of exercise sheets.
Deviations in the first week (of each of the two parts)
- On Monday, 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, on Monday, the concept of the lecture will be discussed. If there are suggestions for changes in the concept, we can discuss these, too.
Deviations in the last week (of each of the two parts)
- Monday 14-16h: Only (2) and (3) applies, (1) is omitted.
- Monday 16-18h: The tutorial takes place, instead of Wednesday.
- Wednesday 14-16h: The exam takes place.
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; Neyman's 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 (on Wednesday).
- 2. Asymptotic Mathematical Theory of Statistics
This part is also organized 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 testContiguity; Optimality theory in LAN experiments
- (Week 6) ML-estimation in DQM families
- (Week 7) Exam for the second half of the course (on Wednesday).
Registration in MUESLI and heiCO
If you are interested in taking the course, please register in MUESLI. Additionally, you need to register in heiCO.
Assignments and exam admission
The lecture is accompanied by weekly assignments which need to be handed in. For examination for each of two parts, it is required to achieve at least 50% in the assigments.
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.
