On a correlation coefficient based on the L₁-norm

The Pearson product-moment correlation coefficient is the most commonly used measure to assess the strength and direction of the linear relationship between a pair of variables. However, it is extremely sensitive to outliers in the data, so it may be necessary to use its robust counterparts. This paper considers a correlation coefficient based on the L₁-norm that has recently been proposed in the literature. Its properties are investigated for the first time and an original computational algorithm is presented, since the index cannot be computed directly but requires an iterative approach. Finally, some illustrative examples are discussed and a comparison with conventional measures is shown.