Maximal Inequalities for Separately Exchangeable Empirical Processes

TL;DR

This paper introduces new maximal inequalities for empirical processes linked to separately exchangeable arrays, providing bounds on moments of their supremum using a novel partitioning technique.

Contribution

It presents the first maximal inequalities for separately exchangeable empirical processes with a new decoupling approach for complex dependencies.

Findings

Established global maximal inequalities for fixed dimension.

Derived refined local maximal inequalities for the first absolute moment.

Applied the technique to general measurable function classes.

Abstract

This paper derives new maximal inequalities for empirical processes associated with separately exchangeable random arrays. For fixed index dimension $K\ge 1$, we establish a global maximal inequality bounding the $q$-th moment ($q\in[1,\infty)$) of the supremum of these processes. We also obtain a refined local maximal inequality controlling the first absolute moment of the supremum. Both results are proved for a general pointwise measurable function class. Our approach uses a new technique partitioning the index set into transversal groups, decoupling dependencies and enabling more sophisticated higher moment bounds.