# NMAK20004U Statistics B

Volume 2020/2021
Education

MSc Programme in Statistics

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
• Asymptotic and finite sample error bounds
• Non-parametric hypotheses about functional relations, e.g. hypotheses about smoothness or shape constraints
• High-dimensional regression including Poisson and logistic regression
• Sparse discrete and Gaussian graphical models

The mathematical content will be presented together with a mix of practical applications demonstrating how the models and methods are used for data analysis.

Learning Outcome

Knowledge:

• Loss functions and risk minimization
• Standard inequalities from probability theory
• Non-parametric model assumptions e.g. via series expansions
• Error bounds under common, non-parametric assumptions, e.g. smoothness, shape constraint or sparsity
• Penalized regression, including ridge regression and lasso
• Graphical lasso

Skills:

• 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

Competences:

• Analysis of complex regression models with a large number of covariates
• Translation between joint models and regression models
• Translation of a scientific hypothesis into either a parametric or a 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 Mathematical Statistics. 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.
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
Written examination, 4 hours under invigilation
...
Exam registration requirements

There will be 3 group assignments (up to two students). The students have to hand-in these assignments, which then need to get approved.

Aid
Written aids allowed
Marking scale