On the mean squared error, the mean absolute error and the like

The problem of finding the minimizer of the rth -mean error , is revisited, via a unified approach. The approach is discussed for arbitrary r and is illustrated for r = 1 (mean absolute error)r = 2 (mean squared error), and r = 4. This approach is also discussed in the context of maximum likelihood estimation in a class of symmetric distributions which includes, among others, the Laplace and the normal distributions.