L1 ESTIMATION IN SMALL SAMPLES WITH LAPLACE ERROR DISTRIBUTIONS

In this paper a Monte Carlo sampling study consisting of four experiments is described. Two error distributions were employed, the normal and the Laplace; and two small sample sizes (20 and 40) were tested. The question of simultaneous-equation bias called for two-stage estimators. The L1, norm was employed as a means of comparing the performance of the L1 or least squares estimators. A relatively new algorithm for computing the direct least absolute (DLA) and two-stage least absolute (TSLA) estimators was employed for the experiments. The results confirmed the hypotheses that for non-normal error distributions such as the Laplace the least absolute estimators were better.