%0 Journal Article %T A Comparison of the Estimators of the Scale Parameter of the Errors Distribution in the L<sub>1</sub> Regression %A Carmen D. Saldiva de Andr¨¦ %A Silvia Nagib Elian %J Open Journal of Statistics %P 261-276 %@ 2161-7198 %D 2022 %I Scientific Research Publishing %R 10.4236/ojs.2022.122018 %X The L₁ regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L₁ estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameter¦Ó. This parameter is such that ¦Ó²/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of ¦Ó. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model.