A nonparametric independence test using random permutations

TL;DR

This paper introduces a novel nonparametric independence test for continuous variables based on the longest increasing subsequence of a permutation, providing exact distribution calculations and demonstrating its effectiveness through simulations.

Contribution

It presents a new independence test leveraging permutation-based statistics with exact distribution calculations, advancing nonparametric testing methods.

Findings

Exact distribution of the test statistic for various sample sizes

The test shows good power under diverse alternative hypotheses

Simulation results validate the effectiveness of the proposed method

Abstract

We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence assumption between the two continuous variables with the space of permutation equipped with the uniform distribution and we show the exact distribution of the statistic. We calculate the distribution for several sample sizes. Through a simulation study we estimate the power of our test for diverse alternative hypothesis under the null hypothesis of independence.