NMAK20004U Statistics B
MSc Programme in Statistics
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.
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
See Absalon for a list of course literature.
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.
- Category
- Hours
- Lectures
- 28
- Preparation
- 115
- Exercises
- 28
- Exam
- 35
- Total
- 206
As
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- Credit
- 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
- 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
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
25 minutes oral exam without preparation time. No aids allowed. If the mandatory assignments have not been approved during the course the non-approved assignment(s) must be handed in no later than three weeks before the beginning of the re-exam week. The assignments must be approved before the re-exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK20004U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- B
- Course capacity
- No limit
The number of seats may be reduced in the late registration period - Course is also available as continuing and professional education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Niklas Andreas Pfister (2-7173437064776b316e7831676e)
Lecturers
Niklas Pfister