ST521: Mathematical Statistics
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to have knowledge of the material from MM533 Mathematical and numerical analysis.
Course introduction
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
Content
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
Examination regulations
Exam element a)
Timing
Tests
Project and written exam
EKA
Assessment
Grading
Identification
Language
Examination aids
To be announced during the course
ECTS value
Additional information
The project weights 20 % of the total grade.
The examination form for re-examination may be different from the exam form at the regular exam.