Graphical tests of independence for general distributions

TL;DR

This paper introduces two flexible, permutation-based graphical tests for assessing independence between two variables across diverse distributions, providing intuitive visual insights and demonstrating effectiveness through simulations and real-world data applications.

Contribution

The paper presents novel, model-free tests of independence that are applicable to any bivariate distribution and offer graphical interpretation of the results.

Findings

Tests perform well in simulations compared to established methods

Graphical outputs help identify specific dependent quantile regions

Effective in real datasets with categorical and mixed data types

Abstract

We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy tails, \ldots The tests take advantage of the recent development of the global envelope tests in the context of spatial statistics. Apart from the broad applicability of the tests, their main benefit lies in the graphical interpretation of the test outcome: in case of rejection of the null hypothesis of independence, the combinations of quantiles in the two marginals are indicated for which the deviation from independence is significant. This information can be used to gain more insight into the properties of the observed data and as a guidance for proposing more complicated models and hypotheses. We assess the performance of the proposed tests in a simulation study and compare them to several well-established tests of independence. Furthermore, we illustrate the use of the tests and the interpretation of the test outcome in two real datasets consisting of meteorological reports (daily mean temperature and total daily precipitation, having an atomic component at 0 millimeters) and road accidents reports (type of road and the weather conditions, both variables having categorical distribution).