Nonparametric Testing for Heterogeneous Correlation

TL;DR

This paper compares two nonparametric rank-based tests designed to detect subpopulation heterogeneity in correlation, demonstrating their effectiveness through an application to wine quality data.

Contribution

It introduces and compares two nonparametric testing procedures for detecting heterogeneous correlations in large datasets, with one adapting to general alternatives.

Findings

Both tests maintain their level against Gaussian copulas.

The tests effectively detect heterogeneity in wine chemical properties.

The adaptive test performs well with complex alternative hypotheses.

Abstract

In the presence of weak overall correlation, it may be useful to investigate if the correlation is significantly and substantially more pronounced over a subpopulation. Two different testing procedures are compared. Both are based on the rankings of the values of two variables from a data set with a large number n of observations. The first maintains its level against Gaussian copulas; the second adapts to general alternatives in the sense that that the number of parameters used in the test grows with n. An analysis of wine quality illustrates how the methods detect heterogeneity of association between chemical properties of the wine, which are attributable to a mix of different cultivars.