A similar thing is using least squares for linear regression rather than minimizing MAD. In past the argument was that the least squares sum has a closed expres

A similar thing is using least squares for linear regression rather than minimizing MAD. In past the argument was that the least squares sum has a closed expression, but with computers even that advantage eliminated. The nice thing about minimizing MAD is that in typical settings the liner regression line-plane-hyperplane goes through measurement points. As such there is no interpolation and outliers are nicely cut off making the result very robust to measurements errors.