ST807: Mathematical Statistics (5 ECTS)

STADS: 15009401

Level
Master's level course

Teaching period
The course is offered in the autumn semester.
The course is offered when needed.

Teacher responsible
Email: bentj@stat.sdu.dk

Timetable
There is no timetable available for the chosen semester.

Comment:
Ubegrænset deltagerantal. Kurset kører i 1. kvartal.

Prerequisites:
None

Academic preconditions:
The material of the courses ST502 Statistical Modeling and ST505 Statistical Simulation is assumed known. It would be an advantage to have followed MM506/MM812 Probability Theory I.

Course introduction
To study the methods and results of mathematical statistics, and their applications in statistical inference.

Expected learning outcome
At the end of the course the student is expected to:

• know the basic concepts of mathematical statistics, such as the likelihood function, score function, information matrix, sufficiency and ancillarity.
• know the basic optimality results of mathematical statistics, such as Cramer-Rao's inequality and the optimality of the likelihood ratio test.
• know the asymptotic theory for likelihood-based inference methods.
• apply the methods and results of mathematical statistics in statistical inference for parametric statistical models.

Subject overview

• Summary of convergence notions and the Central Limit Theorem.
• Statistical models and likelihood functions.
• The score function and Fisher’s information matrix.
• Sufficiency and ancillarity.
• Maximum likelihood estimation and other estimation methods.
• Cramer-Rao's information inequality, and efficiency.
• Consistency and asymptotic normality of the maximum likelihood estimator.
• The likelihood ratio test and other forms of hypothesis tests.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Project concluded by a written report. External examiner. Grade according to the 7-point scale.

The evaluation form can be different for re-exam.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 28 timer
Eksaminatorietimer/opgaveregning: 22 timer
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.