Mean absolute error and root mean square error: which is the better metric for assessing model performance?

such that RMSE includes both the MAE as well as additional information related to the variance (biased estimator) of the errors ε with sample size k. The greater sensitivity of RMSE to a small number of outliers is directly attributable to the variance of absolute error. Further statistical properties for both metrics are derived and compared based on the assumption that the errors are Gaussian. For an unbiased (or bias corrected) model both MAE and RMSE are shown to estimate the total error standard deviation to within a constant coefficient such that