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Empirical Process Theory Reading Group

Organisers

Alexander Kent and Alberto Bordino 


About the reading group

We are interested in the theory of empirical processes. We will follow the lecture notes by Bodhi Sen from Columbia University: A Gentle Introduction to Empirical Process Theory and Applications. Further material can be found in Wellner's lecture notes.


Location and Time

Where: MB2.22
When: 3-4pm on Wednesdays


Timetable

Volunteers are always appreciated! To volunteer for a topic, modify this spreadsheet according to your preferences or inform one of the organisers. Whilst you should follow the relevant section of the lecture notes, we encourage you to include additional content from other sources if you think the content is relevant and interesting and there is time to include it.

Date Topic Presenter
11/01/23 Introduction (Chapter 1) Alexander Kent
18/01/23 Concentration Inequalities (Chapter 3.2 and 13) Alberto Bordino 
25/01/23 Complexity of Function Classes (Chapter 2) Rui Feng
01/02/23 Glivenko-Cantelli (GC) Classes (Chapter 3 - first part) Tom Berrett
08/02/23 Glivenko-Cantelli (GC) Classes (Chapter 3 - second part) Alberto Bordino
15/02/23 Chaining and uniform entropy (Chapter 4) Alexander Kent

References

- Wainwright, M. (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.

-Giné, E., & Nickl, R. (2015). Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.

- van de Geer, S. A. (2000). Applications of empirical process theory, vol. 6 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.

- Pollard, D. (1990). Empirical processes: theory and applications. NSF-CBMS Regional Conference Series in Probability and Statistics, 2, Institute of Mathematical Statistics, Hayward, CA.