Pierre Nyquist: Empirical processes and the Central Limit Theorem

Associated with a sequence of random variables is an object called the empirical process. The goal of this talk is to give a gentle introduction to empirical processes and some related concepts such as uniform versions of the Central Limit Theorem (CLT). In particular, I will discuss the so-called Delta Method and what happens when we move from sequences of real-valued random variables to a more general setting. I will finish with some examples of statistical applications.

The talk will be accessible to anyone with only a basic understanding of random variables and probability theory. In particular, measure theoretic probability is by no means required.