Least sum of absolute deviations regression is considered as a robust alternative to least sum of squared deviations regression. A simple example of linear regression utilizing one predictor variable and a single extreme value illustrates the potential effects of distance, leverage, and influence on the two regression models.
Get full access to this article
View all access options for this article.
References
1.
BarrodaleI., & RobertsF. D. K. (1973) An improved algorithm for discrete L1 linear approximation. Society for Industrial and Applied Mathematics Journal on Numerical Analysis, 10, 839–848.
2.
BarrodaleI., & RobertsF. D. K. (1974) Algorithm 478: solution of an overdetermined system of equations in the L1 norm. Communications of the Association for Computing Machinery, 17, 319–320.
3.
DielmanT. E. (1986) A comparison of forecasts from least absolute value and least squares regression. Journal of Forecasting, 5, 189–195.
4.
DielmanT. E. (1989) Corrections to a comparison of forecasts from least absolute value and least squares regression. Journal of Forecasting, 8, 419–420.
5.
DielmanT. E., & PfaffenbergerR. (1988) Least absolute value regression: necessary sample sizes to use normal theory inference procedures. Decision Sciences, 19, 734–743.
6.
MathewT., & NordströmK. (1993) Least squares and least absolute deviation procedures in approximately linear models. Statistics & Probability Letters, 16, 153–158.
7.
PfaffenbergerR., & DinkelJ. (1978) Absolute deviations curve-fitting: an alternative to least squares. In DavidH. A. (Ed.), Contributions to survey sampling and applied statistics. New York: Academic Press. Pp. 279–294.
8.
RousseeuwP. J. (1984) Least median of squares regression. Journal of the American Statistical Association, 79, 871–880.
9.
TaylorL. D. (1974) Estimation by minimizing the sum of absolute errors. In ZarembkaP. (Ed.), Frontiers in econometrics. New York: Academic Press. Pp. 169–190.
10.
WilsonH. G. (1978) Least squares versus minimum absolute deviations estimation in linear models. Decision Sciences, 9, 322–335.
