NMAK16021U Weak Convergence of Probability Measures
MSc Programme in Statistics
Weak convergence of
probability measures on metric spaces,
both separable and
non-separable. Donsker's theorem on weak
convergence of empirical
distributions to Gaussian
processes. Statistical
applications.
Knowledge:
* Convergence-concepts for probability measures on
infinite-dimensional spaces
Skills: Ability to
* prove and utilize uniform variants of the law of large numbers
* Establish weak convergence to a stochastic
process by combining
weak convergence of finite dimensional
distributions with
combinatorical control.
* use arguments based on chaining
Comptences: Ability to
* explain the significans of working with smaller
sigma-algebras
than the Borel algebra on non-separable spaces,
and master the
corresponding technical complications.
* derive asymptotic distributions for simple
functionals of iid
processes using weak convergence in
function spaces.
certain types of classes active participation is expected.
- Category
- Hours
- Exam
- 31
- Lectures
- 28
- Preparation
- 133
- Theory exercises
- 14
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minwith 30 min preparation time
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
- Re-exam
Same as ordinary
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
- NMAK16021U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C
- Course capacity
- No restrictions/ no limitations
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Ernst Hansen (8-68756b6471766871437064776b316e7831676e)