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

TL;DR

This paper establishes precise clustering rates and Chung-type limit laws for empirical and quantile processes, advancing the understanding of their asymptotic behaviors in the context of functional laws of the iterated logarithm.

Contribution

It provides exact clustering rates and Chung-type limit laws for empirical and quantile processes, extending previous results to new classes of functions and increments.

Findings

Exact clustering rates for empirical and quantile processes

Functional Chung-type limit laws for local empirical processes

Results applicable to functions on the border of the Strassen set

Abstract

Following the works of Berthet (1997), 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.