Clustering rates and Chung type functional laws of the iterated logarithm for empirical and quantile processes

Abstract

Following the works of Berthet [2, 3], we first obtain exact clustering rates in the functional law of the iterated logarithm for the uniform empirical and quantile processes and for their increments. In a second time, we obtain functional Chung-type limit laws for the local empirical process for a class of target functions on the border of the Strassen set.