ST521: Mathematical Statistics (10 ECTS)

STADS: 25003101

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: zimmermann@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.

Prerequisites:
None.

Academic preconditions:
Students taking the course are expected to have knowledge of the material from MM533 Mathematical and numerical analysis.

Course introduction
The aim of the course is to enable the student to understand the theory and methods of mathematical statistics, which is important in regard to master the use of these for practical data analysis.

The course builds on the knowledge acquired in the course MM533
Mathematical and numerical analysis, and gives a general introduction into the area of mathematical statistics and as such forms the basis for subsequent statistics courses, like e.g. computational statistics, multivariate analysis, linear models  and probability theory, as well as for a possible bachelor project in statistics.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Give the competence to master the theories and methods of mathematical statistics, as well as their application to statistical inference
• Give skills to perform statistical analysis of data and critically argue for the choice between relevant models for analysis and solution
• Give theoretical knowledge and practical understanding of the application of methods and models in mathematical statistics

Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:

• master the theory and methods of mathematical statistics
• master the application of these in statistical inference

Subject overview
The following main topics are contained in the course:

• 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

Educational form

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.