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.
MSc Programme in Statistics
- 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 a non-parametric mathematical hypothesis
4 hours lectures and 4 hours of exercises per week for 7 weeks.
See Absalon for a list of course literature.
Probability theory and mathematical statistics equivalent to the
courses Measure and Integrals and Mathematical Statistics. Linear
Algebra at least at the level of the BSc course LinAlgMat
(NMAB10006U). Knowledge of conditional distributions as covered in
either Graphical models or Statistics A.
It is recommended that the course Regression is taken no later than at the same time as this course.
Academic qualifications equivalent to a BSc degree is recommended.
- 7,5 ECTS
- Type of assessment
Written examination, 3 hours under invigilationIn 2021/2022 the exam will be held as an ITX-analogue exam. This means that the exam assignment will be handed out electronically via the ITX-computer, while the students’ hand-in must be written with pen and paper
- Written aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 3
- 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)
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Courseinformation of students