On the Permutation Distribution of Independence Tests

TL;DR

The paper proposes a saddlepoint approximation method for permutation-based independence tests, providing more accurate p-value calculations without extensive simulations, applicable to various rank-based statistics.

Contribution

It introduces a saddlepoint approach for permutation distributions of independence tests, improving p-value accuracy and computational efficiency.

Findings

Saddlepoint approximation closely matches permutation distribution.

Method reduces computational effort compared to simulations.

Applicable to a wide class of rank-based independence tests.

Abstract

One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic, Fisher-Yates statistic, weighted Mann statistic and others. Under the null hypothesis of independence these test statistics have a permutation distribution that usually the normal asymptotic theory used to approximate the p-values for these tests. In this note we suggest using a saddlepoint approach that almost exact and need no extensive simulation calculations to calculate the p-value of such class of tests.