Stat210b: Theoretical Statistics Lecture 13: Empirical Central Limit Theorems

This lecture will complete our coverage of empirical process theory. We will state without proof a more abstract version of the Donsker Theorem, that is covered in detail in (Pollard, 1984, §7.5), and supply two examples of its application. 1 Setup Recall the entropy integral from last lecture, where we developed the Chaining Lemma for checking the conditions for stochastic equicontinuity.