Mathematical statistics

Course goals

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Content

Course Content 
This course gives an introduction to the mathematical theory of statistical inference. Emphasis will be on fundamental notions and methods of statistics. Nevertheless, concrete examples will be given in order to illustrate how the most common methodologies are used in practice.

Learning Objectives 
Subjects:

• statistical model.
• survey sampling.
• concepts of convergence and limit theorems.
• consistency.
• sufficient and complete statistics.
• confidence-region.
• method of moments and maximum-likelihood estimation
• Cramer-Rao lower boundary.
• parametric/ non-parametric statistical tests.
• likelihood ratio test.
• regression models.

Skills: After completing the course, the student knows

• the concept of a sample
• the concept of parametric estimation
• the method of moments
• the maximum likelihood estimator
• concepts of convergence
• sufficient and complete statistics
• confidence-sets
• Fisher information
• Cramer-Rao lower boundary
• statistical tests
• likelihood ratio test
• regression models
• how to analyse a given data set and to interpret the results.

Teaching Methods 
Two times 2 hours of lectures per week and two times 2 hours of exercise class per week.

Assessment

• 20% hand-in exercises 
• 80% exam.

Resit and Effort Requirement 
Students with a final grade >=4 are eligible to do the retake exam. The hand-in counts for the retake as well.

Language
The course is taught in English.