Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not

Abstract. The root-mean-squared error (RMSE) and mean absolute (MAE) are widely used metrics for evaluating models. Yet, there remains enduring confusion over their use, such that a standard practice is to present both, leaving it the reader decide which more relevant. In recent reprise 200-year debate Willmott Matsuura (2005) Chai Draxler (2014) give arguments favoring one metric or other. However, this comparison can false dichotomy. Neither inherently better: RMSE optimal normal (Gaussian) errors, MAE Laplacian errors. When errors deviate from these distributions, other superior.