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 (8 credits points) at the end of the course as well as assignments (2 credit points) in accordance with instructions at course start.