Study Group on Empirical Porcesses for Stochastic Optimization, Spring 2023
Contact: R. Pasupathy (pasupath at purdue dot edu)
Appointed Time: Each Wednesday at 4:00 pm eastern.
Zoom Link: Zoom link

Description

Empirical process theory (EPT) is said to be the great unifier of modern statistics. In this series of meetings, we will study EPT with a view toward its use in stochastic optimization, which in a sense subsumes M-estimation in classical statistics.

Schedule

lecture number 1 Wednesday, 01/25, 4:00 pm -- 5:00 pm (Pasupathy) motivation notes
lecture number 2 Wednesday, 02/01, 4:00 pm -- 5:30 pm (Pasupathy) motivation notes
lecture number 3 Wednesday, 02/08, 4:00 pm -- 5:30 pm (Yip) empirical processes, introduction notes comment on KS statistic
lecture number 4 Wednesday, 02/15, 4:00 pm -- 5:30 pm (Yip) empirical processes, introduction notes Pakes&Pollard
lecture number 5 Wednesday, 02/22, 4:00 pm -- 5:30 pm (Chu) ULLN Classes
lecture number 6 Wednesday, 03/01, 4:00 pm -- 5:30 pm (Chu) ULLN Classes
lecture number 7 Wednesday, 03/08, 4:00 pm -- 5:30 pm (Pasupathy) Uniform CLT notes
lecture number 8 Wednesday, 02/22, 4:00 pm -- 5:30 pm (Yu) Consistency
lecture number 9 Wednesday, 03/01, 4:00 pm -- 5:30 pm (Yu) Consistency
lecture number 10 Wednesday, 02/22, 4:00 pm -- 5:30 pm (Zhou) Convergence Rate
lecture number 11 Wednesday, 03/01, 4:00 pm -- 5:30 pm (Zhou) Convergence Rate
lecture number 12 Wednesday, 03/08, 4:00 pm -- 5:30 pm (Pasupathy) The Bootstrap

References and Other Useful Documents

Prelimaries on Metric Spaces (also see Appendix M in B1999) preliminaries
Patrick Billingsley (1999). Convergence of Probability Measures. Wiley.
van der Vaart and Wellner (1996). Weak Convergence and Empirical Processes. Wiley.
Gine and Nickl (2016). Mathematical Foundations of Infinite Dimensional Models. Wiley.
van de Geer (2000). Empirical Processes in M-Estimation. Wiley.
DasGupta (2011). Probability for Statistics and Machine Learning. Springer.