Inference for high-dimensional exchangeable arrays

TL;DR

This paper develops new statistical inference methods for high-dimensional exchangeable arrays, including central limit theorems and bootstrap techniques, with applications to density estimation and network analysis.

Contribution

It introduces novel high-dimensional CLTs and multiplier bootstrap methods for exchangeable arrays, supported by new technical tools and theoretical guarantees.

Findings

Methods achieve precise uniform coverage rates in simulations

Applications include confidence bands for density estimation

Illustration with international trade network densities

Abstract

We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. These theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We exhibit applications of our methods to uniform confidence bands for density estimation under joint exchangeability and penalty choice for $\ell_1$-penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.