# Statistics B

### Course 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.

Education

MSc Programme in Statistics

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 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
• 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.

Written
Oral
ECTS
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
In 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
Aid
Written aids allowed
Marking 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)

• Category
• Hours
• Lectures
• 28
• Preparation
• 115
• Exercises
• 28
• Exam
• 35
• English
• 206

### Kursusinformation

Language
English
Course number
NMAK20004U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 3
Schedulegroup
B
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Niklas Andreas Pfister   (2-7d7f4f7c7083773d7a843d737a)
##### Teacher

Niklas Pfister

Saved on the 25-03-2022

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