Weighted Lasso Subsampling for HighDimensional Regression

Abstract

Lasso regression methods are widely used for a number of scientic applications.Many practitioners of statistics were not aware that a small changein the data would results in unstable Lasso solution path. For instance, inthe presence of outlying observations, Lasso perhaps leads the increase inthe percentage of the false selection rate of predictors. On the other hand,the discussions on determining an optimal shrinkage parameter of Lasso isstill ongoing. Therefore, this paper proposed a robust algorithm to tacklethe instability of Lasso in the presence of outliers. A new weight function isproposed to overcome the problem of outlying observations. The weightedobservations are subsamples for a certain number of subsamples to controlthe false Lasso selection. The simulation study has been carried out and usesreal data to assess the performance of our proposed algorithm. Consequently,the proposed method shows more eciency than LAD-Lasso and weightedLAD-Lasso and more reliable results.