# Syllabus for Theoretical Statistics DS

Teoretisk statistik DS

## Syllabus

• 7.5 credits
• Course code: 1MS039
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Mathematics A1N, Data Science A1N
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2022-03-03
• Established by: The Faculty Board of Science and Technology
• Applies from: Autumn 2022
• Entry requirements:

120 credits including 90 credits in mathematics. Participation in Inference Theory II. Proficiency in English equivalent to the Swedish upper secondary course English 6.

• Responsible department: Department of Mathematics

## Learning outcomes

On completion of 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 (5 credits) at the end of the course as well as assignments (2.5 credit) during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

## Other directives

This course cannot be included in the same degree as the course ​1MS033.

Applies from: Autumn 2022

Some titles may be available electronically through the University library.

• van der Vaart, A. W. Asymptotic Statistics

Cambridge University Press, 2000

Mandatory

• Liero, Hannelore; Zwanzig, Silvelyn Introduction to the theory of statistical inference

Boca Raton, FL: CRC Press, 2012

Find in the library

Mandatory