Mathematical Statistics

15 credits

Syllabus, Master's level, 1MS013

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MS013
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, 6 November 2007
Responsible department: Department of Mathematics

Entry requirements

120 credit points Inference Theory

Learning outcomes

In order to pass the course (grade 3) the student should

have a theoretical foundation in mathematical statistics sufficient for further studies at advanced level and for a future professional career as a mathematical statistician;

possess a deeper knowledge in probability theory, in particular regarding multidimensional stochastic variables and their transforms, and have thorough experiences of conditional probabilities and expectations;

be able to give an account of and perform computations with the multidimensional normal distribution;

be able to use transform methods as a tool for studying stochastic variables and their distributions;

be familiar with central limit theorems and several of their applications;

possess a deeper knowledge of principles and basic methods for statistical inference;

be able to use a number of methods for parameter estimation and to give an account of their theoretical properties and practical applicability;

know the theoretical basis for hypothesis testing and be able to perform several variants of hypothesis tests;

possess a deeper knowledge of the linear model, in particular linear regression and analysis of variance.

Content

Probability theory: multidimensional stochastic variables and distributions, conditioning, ordering variables, concepts of convergence in probability theory, multidimensional normal distribution, transforms and their use, central limit theorems and their applications.

Inference theory: statistical models; principles of inference based on likelihood, Fisher information and sufficiency; estimation and estimation methodology, Cramér–Rao's inequality, optimality; test of hypothesis, Neyman Pearson test, uniformly most powerful tests; linear models, the Gauss– Markov theorem, least squares methods.

Instruction

Lectures and problem solving sessions.

Assessment

Separate written examinations in Probability Theory (7 credit points) and Inference Theory (7 credit points) at the end of the course, and an oral examination in Probability Theory (1 credit point). Assignments given during the course may be credited as parts of the final written tests.