This course provides a rigorous overview of selected topics in Statistical Decision Theory for PhD students interested in understanding and contributing to the mathematical statistics or, e.g., theoretical eonometrics literature. More specifically, we shall consider the following topics:

• Statistical models: divergences, L2 differentiability, tests in binary models.
• General decision problems: risk, Bayes and minimax decisions, complete classes.
• Large sample approximations of models and decisions.
• Testing.
• Selection problems.

Students interested in statistical decision problems arising in, e.g., economics, finance or computer science are welcome to attend the course. There is some freedom as to which topics we shall go through. Adapting to individual student's interests is possible.

Studends develop a rigorous understanding of the formal methods in statistical decision theory and develop a detailed understanding of some of its subareas.

For this course participation is obligatory. Students are allowed to miss a maximum of 20% (no matter if excused or not excused).

This course is taught as lectures with assignments and a written final exam. In combination with the lectures, the assignments help students to consolidate and expand their understanding of the topics discussed in the lectures.

Grading is based on assignments (5 assignments à 12%) and a written final exam (40 %).

• 1 if final score >= 0.9
• 2 if final score < 0.9 and >=0.75
• 3 if final score < 0.75 and >=0.65
• 4 if final score < .65 and >=0.55
• 5 if final score < 0.55

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To follow the course, a good understanding of econometrics/statistics and probability (CLT, LLN) is necessary. An interest in formal arguments and in the mathematics underlying statistical decision making is necessary.