Entry requirements

120 credit points including 90 credit points of Mathematics. Real Analysis recommended.

Learning outcomes

In order to pass the course the student should be able to

• understand the principles of optimal estimation;
• understand the theory of optimal tests, especially unbiased and invariant tests;
• describe the decision theory;
• understand the principles of the asymptotic behaviour of statistical methods, especially the asymptotic efficiency;
• using the delta method , including the functional delta method;
• understand 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. The assignments can be registered as part of the written examination.