Study Group on Empirical Processes, Spring 2021
Current Group Members: A. DasGupta, M. Levine, T. Owada, R. Pasupathy, J. Xie, and T. Zhang
Contact: R. Pasupathy (pasupath at purdue dot edu)
Join seminar at appointed time: Zoom link

Lecture Schedule

lecture number 1 | Friday, 02/19, 4:00 pm (Pasupathy) | why empirical processes? | lecture notes
lecture number 2 | Friday, 03/05, 4:00 pm (Pasupathy) | weak convergence in C[0,1], Donsker's theorem | lecture notes
lecture number 3 | Friday, 03/19, 4:00 pm (Andrew Thomas) | weak convergence in D[0,1], Skorohod metric | lecture notes
lecture number 4 | Friday, 04/02, 4:00 pm (Pasupathy) | emp. processes, Donsker and Glivenko-Cantelli classes | lecture notes
lecture number 5 | Friday, 04/16, 4:00 pm (Pasupathy) | Glivenko-Cantelli using chaining, symmetrization, VC classes | lecture notes
lecture number 6 | Friday, 04/30, 4:00 pm (Pasupathy) | VC classes, Glivenko-Cantelli for MLE, regression

Useful References

Patrick Billingsley (1999). Convergence of Probability Measures. Wiley.
Anirban DasGupta (2011). Probability for Statistics and Machine Learning. Springer.
Michael M. Kosorok (2008). Introduction to Empirical Processes and Semiparametric Inference. Springer.
Robert J. Serfling (1980). Approximation Theorems of Mathematical Statistics. John Wiley and Sons.
Galen A. Shorack and Jon. A. Wellner (2009). Empirical Processes with Applications to Statistics. SIAM.