NMAK20004U Statistics B
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
The course covers a number of modern statistical models and methods, mathematical methods for analyzing them, and mathematical relations between the different methods.
The course will cover the following content
Elements of statistical decision theory
Regularization for high-dimensional and non-parametric regression
Kernel methods and reproducing Hilbert space theory
Concentration inequalities and their relation to finite sample error bounds
Sparsity and high-dimensional theory
The focus of this course is on the mathematical foundations of modern statistical methods. The content will be presented with a focus on statistical guarantees that can be achieved with these methods.
Loss functions and risk minimization
Statistical modeling and (asymptotic) optimality theory
Standard inequalities from probability theory
Non-parametric model assumptions via kernel methods
Penalized regression, including ridge regression and lasso
Error bounds under common, non-parametric assumptions, e.g. smoothness or sparsity
Perform theoretical analyses of statistical methods under parametric or non-parametric model assumptions.
Discuss the limitations of the models and methods covered.
Derive error bounds based on the theory covered.
Ability to interpret theoretical results in the context of practical data analysis, including how complex models with many covariates can be analyzed and the results interpreted.
Analysis of complex regression models with a large number of covariates
Assess which statistical guarantees are available for the covered methods.
Translation of a scientific hypothesis into either a parametric or non-parametric mathematical hypothesis.
See Absalon for a list of course literature.
It is recommended that the course Regression is taken prior to this course.
Academic qualifications equivalent to a BSc degree is recommended.
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- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilation
- Exam registration requirements
There will be 3 group assignments (up to three students). The students have to hand-in these assignments, which then need to get approved.
- Written aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
25 minutes oral exam without preparation time. No aids allowed. If the mandatory assignments have not been approved during the course the non-approved assignment(s) must be handed in no later than three weeks before the beginning of the re-exam week. The assignments must be approved before the re-exam.
Criteria for exam assesment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
- Course code
- 7,5 ECTS
- Full Degree Master
- 1 block
- Block 3
- Course capacity
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Niklas Andreas Pfister (2-7d7f4f7c7083773d7a843d737a)