Uniform Central Limit Theorems for pregaussian classes of functions
Uniform Central Limit Theorems for pregaussian classes of functions
<!-- *** Custom HTML *** --> We study weak convergence of general (smoothed) empirical processes indexed by classes of functions $\mathcal{F}$ under minimal conditions. We present a general result that, applied to specific situations, enables us to prove uniform central limit theorems under <i>P</i>-pregaussian assumption on $\mathcal{F}$ only.