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
MSc Programme in Mathematics-Economics
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.
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 StatMet and MStat (alternatively
“MatStat” from previous years) Linear Algebra at least at the level
of the BSc course LinAlgMat (NMAB10006U). Knowledge of conditional
distributions as covered in either Statistics A or Graphical Models
from previous years.
It is recommended that the course Regression is taken prior to this course.
Academic qualifications equivalent to a BSc degree is recommended.
- 7,5 ECTS
- Type of assessment
Written examination, 3 hours under invigilation
- Type of assessment details
- 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