A permutation test for matching and its asymptotic distribution

TL;DR

This paper introduces a permutation test to assess the significance of observed similarities in paired data, providing an explicit normal approximation with bounds for determining critical levels under the null hypothesis.

Contribution

It develops a permutation testing framework for matching problems and derives an asymptotic normal distribution with explicit bounds for the test statistic.

Findings

Normal approximation with explicit bounds for the permutation test

Applicable to situations with unknown baseline similarity

Provides a method for testing the significance of pairings

Abstract

We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null hypotheses where there is no distinguished pairing of the observations, a normal approximation with explicit bounds and rates is presented for determining approximate critical test levels.