On the Consistency of the Crossmatch Test

TL;DR

This paper proves the consistency of Rosenbaum's crossmatch test for two-sample goodness-of-fit across all fixed alternatives, extending its theoretical foundation.

Contribution

It establishes the first proof of the test's consistency against all fixed alternatives and develops a general consistency framework.

Findings

The crossmatch test is consistent against all fixed alternatives.

A general consistency result applicable to similar tests is developed.

Theoretical validation enhances the test's reliability in practice.

Abstract

Rosenbaum (2005) proposed the crossmatch test for two-sample goodness-of-fit testing in arbitrary dimensions. We prove that the test is consistent against all fixed alternatives. In the process, we develop a general consistency result based on (Henze & Penrose, 1999) that applies more generally.