ST521: Mathematical Statistics

Students taking the course are expected to have knowledge of the material from MM533 Mathematical and numerical 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

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

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

These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

• Intro phase (lectures) - 60 hours
• Training phase: 60 hours