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ST521: Mathematical Statistics (10 ECTS)

STADS: 25003101

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: bentj@stat.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 14-16 U155 36-41,43-46,48-51
Common I Tuesday 08-10 U157 36,47
Common I Thursday 10-12 U155 36-41,43-51
H1 TE Monday 12-14 U153 44
H1 TE Wednesday 08-10 U156 37-41,43-51
H1 TE Thursday 12-14 U183 46
H1 TE Friday 08-10 U157 36-41,43,45-51
O1 TE Monday 10-12 U148 44 Eksaminatorier
O1 TE Wednesday 12-14 U141 37-41,43-51
O1 TE Friday 12-14 U69A 36-41,43,45-51
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Comment:
Ubegrænset deltagerantal. Samlæses med ST517

Prerequisites:
None

Academic preconditions:
The material from MM533 Mathematical and numerical analysis or similar is assumed known.  

Students that have passed ST519 Mathematical Statistics (5 ECTS-version) are not allowed to take this course.

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

Qualifications
To master the theory and methods of mathematical statistics, and their applications in statistical inference.

Expected learning outcome
To master the theory and methods of mathematical statistics, and their applications in statistical inference.

Subject overview

  • Probability and random variables.
  • Independence, conditional probability, and Bayes’ Theorem.
  • Discrete and continuous distributions.
  • Expectation, variance and covariance. 
  • Special distributions. 
  • The normal distribution and the Central Limit Theorem. 
  • Moment generating functions. 
  • Modes of convergence and the Law of Large Numbers
  • Likelihood functions and maximum likelihood estimation. 
  • The score function and Fisher’s information matrix.
  • Cramer-Rao's information inequality, and efficiency.
  • Consistency and asymptotic normality of the maximum likelihood estimator.
  • Sufficiency and its use in estimation. 
  • The likelihood ratio test and other forms of hypothesis tests.
  • Statistical inference based on confidence intervals and 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 and written exam. Internal censorship by the Danish 7-mark scale. 10 ECTS.

The project weights 20 % of the total grade.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 60 hours
Skills training phase: 60 hours, hereof:
 - Tutorials: 60 hours

Educational activities Study phase: 10 hours

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.