Minimisation of bias of Pearson correlation coefficient in presence of coincidental outliers

Abstract

It is well known that sample correlation coefficient is a significant statistical measure of linear comovement between variables. However, the distortion that is caused by 'coincidental outliers' is fairly large. For this reason, we suggest an alternative robust measure of correlation that obtains the lowest bias. We formally call this measure the bootstrap-based correlation coefficient. We show analytically that our measure exhibits lower bias with respect to classical estimator. We compare its performance both across the classical estimator and across the robust measures of Kim et al. (2015) applying Monte Carlo simulations. The results verify the outperformance of the bootstrap-based correlation coefficient relatively to other measures, in presence of 'coincidental outliers'.