NMAK24010U Topics in Statistics

Volume 2024/2025
Education

MSc Programme in Statistics
MSc Programme in Mathematics-Economics

Content

The purpose of this course is to introduce the student to the theoretical analysis of nonparametric statistical methods. The essence of the course is several mathematical results both on what is possible and impossible using nonparametric regression and nonparametric hypothesis testing.

The course will cover

  • Nonparametric regression methods
  • Minimax lower bounds for nonparametric regression
  • Nonparametric hypothesis testing
  • Impossibility results for nonparametric hypothesis testing
Learning Outcome

Knowledge:

  • Uniform Type I and II error control for nonparametric hypotheses
  • Error bounds for nonparametric regression estimators under smoothness assumptions
  • Nonparametric unconditional and conditional independence testing
  • Methods for nonparametric regression including their advantages and disadvantages
  • Results on the fundamental limits of nonparametric statistics

 

Skills: Ability to

  • prove upper and lower bounds for a nonparametric regression problem
  • theoretically analyze a nonparametric hypothesis testing problem

 

Competences: Ability to

  • assess whether a nonparametric statistical hypothesis is testable
  • determine whether a nonparametric regression method is optimal for a given distribution
  • give an oral presentation of a specific topic within the theory covered by the course
Experience with theoretical statistics at the level of Statistics B and measure theoretic probability (e.g. at the level of Sand and Sand2).

It is advantageous to also have done Regression and Statistics A to fully appreciate the results of the course.
4 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 156
  • Exercises
  • 21
  • Exam
  • 1
  • Total
  • 206
Oral
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (30-minute preparation time)
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Re-exam

Same as the ordinary exam

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.