Gaussian and Empirical Process Theory for High Dimensional Statistics

Alexander Giessing (University of Washington) , Jiahua Chen (University of British Columbia)

Jan 1, 2023 — Apr 30, 2023

About the course

In this course we develop elements of the theory of Gaussian and empirical processes that have proved useful for statistical inference in high-dimensional models, i.e. statistical models in which the number of parameters is much larger than the sample size. The course consists of three parts, with the first two parts laying the foundation for the third one: an introduction to modern techniques in Gaussian processes, a recap of empirical classical process theory emphasizing weak convergence on metric spaces, and lastly, a discussion of Gaussian approximation, high-dimensional CLTs, and the conditional multiplier bootstrap.

Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
Gaussian and Empirical Process Theory for High Dimensional Statistics
Date
Jan 1, 2023 — Apr 30, 2023
Course Number
Stat 591
Section Number
Section Code

Instructor(s)

For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details

Homework and Examinations

There will be regular homework assignments and an oral examination. The oral examination will work as follows: The lecture will be divided in roughly ten topics which will be shared with the students ahead of time. At the day of the examination the students will randomly draw two topics and give two 10-15 min presentations on their topics on the blackboard (no prepared notes allowed). Each presentation will conclude with ca. 5 minutes of follow-up questions. Textbooks for the first and second part:

  • Dudley, R. M. (2014). “Uniform Central Limit Theorems”. CUP.
  • Giné, E. and Nickl, R. (2016). “Mathematical Foundations of Infinite-Dimensional Statistical Models”. CUP.
  • van der Vaart, A. and Wellner, J. (1996). “Weak Convergence and Empirical Processes”. Springer.

Typed lecture notes of all three parts will be provided.

2022-2023