Abstract
The least absolute deviation (LAD) estimator is an alternative to the ordinary least squares estimator when some outliers exist, or the error term in the regression model has a heavy-tailed distribution. The gist of this chapter is to present a new estimator for sparse and robust linear regression that improves the preliminary test LAD estimator, an estimator which depends on a test decision. Our strategy is to apply auxiliary information in the estimation obtained from employing the LAD-LASSO operator to find the null hypothesis, building the preliminary test estimator and its improvement. A Monte-Carlo simulation study shows that this new estimator is better than others. Moreover, an objective data analysis confirms that our proposed estimator performs better in the prediction error sense than the LAD, LAD-LASSO, and preliminary test estimators.
