Median based robust correlation coefficient

Abstract

Real datasets usually include a fraction of outliers and other contaminations. The classical correlation coefficient is much affected by these outliers and often gives misleading results. The problem of computing the correlation estimate from bivariate data containing a portion of outliers has been deliberated in this study. The classical correlation uses non-robust mean and standard deviation as the location and scale estimator respectively. In this study, two robust correlation coefficients based on high breakdown point median estimator were examined. The performance of the classical correlation together with the robust correlation coefficient was measured and compared in terms of the correlation value, average bias and standard error for the clean and contaminated data. Simulation studies reveal that all correlation coefficients perform well for clean data. However, under contaminated data, the findings show that median based robust correlation coefficient gives better results as compared to the classical correlation coefficient.