Theoretical Statistics
10 credits
Syllabus, Master's level, 1MS033
A revised version of the syllabus is available.
- Code
- 1MS033
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 23 April 2013
- Responsible department
- Department of Mathematics
Entry requirements
120 credits including 90 credits of Mathematics. Inference Theory II.
Learning outcomes
In order to pass the course the student should be able to
- explain the principles of optimal estimation;
- explain the theory of optimal tests, especially unbiased and invariant tests;
- give an account of the decision theory;
- explain the principles of the asymptotic behaviour of statistical methods, especially the asymptotic efficiency;
- use the delta method, including the functional delta method;
- explain the use of projection in statistics especially in linear regression and variance analysis.
Content
Maximum likelihood-estimator, James Stein-estimator, M-estimators, optimality of the F-test, minimax tests, asymptotic efficiency, LAN-model, U-statistics, Hajek projection, linear models.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course combined with compulsory assignments.