Description
The linear regression model predicts the response variable (y) as a linear function (combination) of one or more predictors. The least-squares method assumed that the response variable follows a normal distribution. However, this method is sensitive to outliers or heavy-tailed distributions, while the Least absolute deviation (LAD) estimator provides more robust estimates. A popular choice for shrinkage estimation and variable selection is the Least absolute shrinkage and selection operator (LASSO). The Scaled-LASSO (SLASSO) was proposed by pre-multiplying LASSO with a matrix term. The estimator dominates LASSO for shrinkage estimation but does not perform variable selection. Thus, in this study, the LAD estimator is combined with the SLASSO to develop a robust penalized variable selection (LAD-SLASSO). We examined the efficiency of the proposed method extensively through simulation studies and real-life applications. The estimated results revealed that the LAD-SLASSO and LAD-LASSO significantly reduce the test mean squared error compared with some existing methods.