Abstract
L<TEX>$_1$</TEX>-estimator in the linear regression model is widely recognized to have superior robustness in the presence of vertical outliers. While the L<TEX>$_1$</TEX>-estimation procedures and algorithms have been developed quite well, less progress has been made with the hypothesis test in the multiple L<TEX>$_1$</TEX>-regression. This article suggests computer-intensive resampling approaches, jackknife and bootstrap methods, to estimating the variance of L<TEX>$_1$</TEX>-estimator and the scale parameter that are required to compute the test statistics. Monte Carlo simulation studies are performed to measure the power of tests in small samples. The simulation results indicate that bootstrap estimation method is the most powerful one when it is employed to the likelihood ratio test.
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