Terry E. Dielman (1986), "A comparison of forecasts from least
absolute value and least squares regression," Journal of Forecasting, 5,
This paper begins with an interesting historical review of regression methods. The
least absolute value (LAV) method as a criterion for best fit was introduced
in 1757. About half a century later, in 1805, regression advanced to least squares. Or was
it an advance? Dielman concludes that, in cases where outliers are expected, LAV provides
better forecasts than does least squares. This conclusion was obtained from the Monte
Carlo simulation results that he reports in this paper. Dielman also concludes that LAV is
more robust than least squares. It is nearly as accurate for data that have normally
distributed errors, and it is significantly more accurate for data with outliers. This
makes me wonder whether the more recent advances in regression, such as ridge regression,
have merely brought us up to the accuracy possible with procedures from the 18th century.
Dielman did not use ridge regression in his comparison, so this is speculation.
Dielmans study should be extended to actual data. In doing so, it would be useful to
make the comparison on data where standard procedures have been used for outliers (e.g.,
trimming or removing outliers prior to analysis).