Syllabus for Theoretical Statistics

Teoretisk statistik

A revised version of the syllabus is available.

Syllabus

  • 10 credits
  • Course code: 1MS033
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Mathematics A1N

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle

    • G1N: has only upper-secondary level entry requirements
    • G1F: has less than 60 credits in first-cycle course/s as entry requirements
    • G1E: contains specially designed degree project for Higher Education Diploma
    • G2F: has at least 60 credits in first-cycle course/s as entry requirements
    • G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    • GXX: in-depth level of the course cannot be classified

    Second cycle

    • A1N: has only first-cycle course/s as entry requirements
    • A1F: has second-cycle course/s as entry requirements
    • A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    • A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    • AXX: in-depth level of the course cannot be classified

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2012-03-08
  • Established by:
  • Revised: 2018-08-30
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: Spring 2019
  • Entry requirements:

    120 credits including 90 credits of Mathematics. 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 (8 credits points) at the end of the course as well as assignments (2 credit points) in accordance with instructions at course start.

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.

Syllabus Revisions

Reading list

Reading list

Applies from: Spring 2020

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

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