Thread: MAE and RMSE

Hi everybody,

Please, can somebody help me in understanding the difference between the MAE and RMSE statistical concepts?

Which of them is the best for assessing the accuracy of the estimator? why?

Thank you so much for your help.

Best,
Nahr Elk

MAE or Mean Absolute Error is the arithmetic mean of the modulus of the difference between each value and the mean, given by $\displaystyle \frac{1}{n}\sum |X_i-\bar{X}|$ and RMSE or Root Mean Square Error is the square root of the average of the sum of the squares of the differences between each value and mean, given by $\displaystyle \sqrt{\frac{1}{n}\sum (X_i-\bar{X})^2$. So, both of them determines the degree of dispersion of the data. You can not say which one is the "best" since both originates from some valid logic, but RMSE is more frequently used than MAE because RMSE (or its square, that is the "variance") is much easier to deal algebraically than MAE. For instance, to make any algebrical operation on MAE, the modulus sign needs to be broken up, unlike RMSE. In that sense, RMSE is more flexible to use than MAE

Hi Sambit,

I am very grateful for your great explanation.
Many thanks