1985-1995 Reviews

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. Dielman’s 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). |