Concentration inequalities and asymptotic results for ratio type empirical processes

Abstract

Let F be a class of measurable functions on a measurable space (S,&) with values in [0, 1] and let P n=n -1∑ i=1nδX i be the empirical measure based on an i.i.d. sample (X 1,...,X n) from a probability distribution P on (S, &). We study the behavior of suprema of the following type: sup rn