# NMAK20004U Statistics B

Volume 2024/2025
Education

MSc Programme in Statistics

MSc Programme in Mathematics-Economics

Content

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.

Learning Outcome

Knowledge:

• 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

Skills:

• Perform theoretical analyses of statistical methods under parametric or non-parametric model assumptions.

• Discuss the limitations of the covered models and methods.

• Derive error bounds based on the covered theory.

• 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.

Competences:

• Analyze complex regression models with a large number of covariates.

• Assess which statistical guarantees are available for the covered methods.

• Translate a scientific hypothesis into either a parametric or non-parametric mathematical hypothesis.

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.
4 hours lectures and 4 hours of exercises per week for 7 weeks.
• Category
• Hours
• Lectures
• 28
• Preparation
• 115
• Exercises
• 28
• Exam
• 35
• Total
• 206
Written
Oral
Credit
7,5 ECTS
Type of assessment
On-site written exam, 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.

Aid
Written aids allowed
Marking scale