Regression models are usually estimated using Ordinary Least Squares (OLS). An alternative method is to minimize the sum of absolute errors between the actual observation and its “predicted” (fitted) value for calibration data, a procedure known as least absolute value estimation (LAV). According to Dielman (1986), the LAV method as a criterion for best fit was introduced in 1757. About half a century later, in 1805, least squares was developed. Using Monte Carlo simulation studies, Dielman concluded that, in cases in which outliers are expected, LAV provides better forecasts than does least squares and is nearly as accurate as least squares for data that have normally distributed errors.
- Dielman, T. E. (1986), "A comparison of forecasts from
least absolute value and least squares regression,"
*Journal of
Forecasting*, 5, 189-195.