Robust Estimation of Straight Line Regression Coefficients by Minimizing pth Power Deviations

It is well known that the mean is very sensitive to deviations from normality, especially due to outliers or long tails. We propose the use of an estimator which has been demonstrated to be more robust than least squares for estimating the simple mean, that is, the estimator which minimizes the pth power of the deviations for a power of p between one and two. We also show that a reasonably fast and widely available computer subroutine is available to solve the problem.