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Recently dmloped large sampk inference procedures for least absolute value (LAW qprssion arc d n e d via Monte Car10 simulation to determine when sample size are large enough for the procedures to work effectively. A variety of different experimental settings were created by varying the disturbance distribution, the number of aplanatory variables and the way the aplanatory variables were generated. Necessary sample sizes range from as small as 2 0 when disturbances arc normal to as large as 200 in atreme outlier-producing distributions. Subject Anos. Llnuu StPMcul Models, Sbnuhtlon, and Statistical lkhniqu-Least squares regression analysis has long been recognized as a useful statistical tool to aid in decision making. The optimal properties of least squares (LS) estimators are known when disturbances are normally distributed. However, when disturbances come from nonnormal distributions the LS estimator may not be the best technique to use in fitting equations to data. Several studies (including [3], [20], [21], and [22]) have shown that the Il-norm, or least absolute value (LAV) estimator, may provide improved estimates of the regression coefficients when disturbances come from fat-tailed or outlier-producing distributions (for example, Cauchy, Laplace, or contaminated normal).LS estimates can be more severely affected by outliers or extreme data points than the LAV estimates. This is due to the weight given each data point by the LS technique when minimizing the sum of squared errors. Since LAV minimizes the sum of the absolute values of the errors, extreme points will not be so influential in determining the regression line or surface.LAV estimation was first suggested by Boscovich [41 fifty years prior to Legendre's announcement of the principle of least squares in 1805. It was not until 1955, however, that the LAV procedure began to attract serious notice from applied researchers. The Charnes, Cooper, and Ferguson (51 article, which first used linear programming to solve the LAV regression problem, proved LAV to be a computationally tractable technique. Bassett and Koenker [2] provided the next necessary step for LAV regression to become a truly useful technique in practice. They developed the large sample distribution of the coefficient estimator under very general conditions. As long as errors are independent and from a symmetric distribution, the coefficient estimator will be asymptotically normal. The variance of the disturbance distribution need not be finite. They also proved that the estimator is consistent. Their results can be used to show that the LAV regression estimator will be more efficient *This papa has benefitted from the comments of two anonymous referees and an associate editor. Any remaining errors are the responsibility of the authors. This research was supported in part by a grant from the M. J. Neeley School of Business, ' k a s Christian University. 734

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