Robust sparse regression and tuning parameter selection via the efficient bootstrap information criteria

Abstract

There is currently much discussion about lasso-type regularized regression which is a useful tool for simultaneous estimation and variable selection. Although the lasso-type regularization has several advantages in regression modelling, owing to its sparsity, it suffers from outliers because of using penalized least-squares methods. To overcome this issue, we propose a robust lasso-type estimation procedure that uses the robust criteria as the loss function, imposing L₁-type penalty called the elastic net. We also introduce to use the efficient bootstrap information criteria for choosing optimal regularization parameters and a constant in outlier detection. Simulation studies and real data analysis are given to examine the efficiency of the proposed robust sparse regression modelling. We observe that our modelling strategy performs well in the presence of outliers.

Keywords:

• efficient bootstrap information criteria
• elastic net
• lasso-type regularization
• least-trimmed squares
• regression model

AMS Subject Classification:

• 62F35
• 62F40
• 62J07

Acknowledgements

The authors thank the associate editor and anonymous reviewer for the constructive and valuable comments that improved the quality of the paper considerably.