Introduction to Empirical Processes

Instructor: Dr. Tung Pham

Description

The course aims to provide an overview of some of the basic tools that empirical process theory has to offer in the study of asymptotic properties of statistical procedures.

Topics include:

• Stochastic convergence.
• Maximal, moment and tail inequalities.
• Symmetrization.
• Glivenko-Cantelli and Donsker classes.
• Vapnik-Chervonenkis dimension, covering and bracketing numbers
• Applications to M-estimators, Z-estimators and delta methods.

For more details see the official course book.

Required prior knowledge

real analysis, probability theory, statistical theory.

Recommended Texts

van der Vaart, A.W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics.

Exam Information

There will be a term paper.