Limit Behaviour of Sequential Empirical Measure Processes

TL;DR

This paper establishes uniform laws of large numbers and central limit theorems for sequential empirical processes indexed by VC-type classes, advancing understanding of their asymptotic behavior.

Contribution

It provides new uniform convergence results and limit theorems for sequential empirical measures indexed by VC classes, extending existing theoretical frameworks.

Findings

Proved uniform laws of large numbers for sequential empirical processes.

Established functional central limit theorems for these processes.

Identified conditions under which these asymptotic results hold.

Abstract

In this paper, we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate Vapnik-Chervonenkis properties.