A Simulation Study for Monotonic Dependence in the Presence of Outliers

This paper aims at examining the performance of a recently proposed measure of dependence – the Monotonic Dependence Coefficient – with respect to classical correlation measures like the Pearson’s product-moment and the Spearman’s rank-order correlation coefficients, using simulated outlier contaminated and non-contaminated datasets as well as a real dataset. The comparison aims at checking how and when these coefficients detect dependence relationships between two variables when outliers are present. Several scenarios are created, contemplating in particular multiple values for the coefficients, multiple outlier contamination percentages, various simulation data patterns, or a combination of these. The basic simulation dataset is generated from a bivariate standard normal distribution. Then, the contaminated data are generated from exponential, power-transformed and lognormal distributions. The main findings tend to favour the Spearman’s rank-order correlation coefficient for most of the scenarios, especially when the contamination is taken into account, whereas MDC performs better than the Spearman’s rank-order correlation coefficient in non-contaminated data.