NOVEL RESAMPLING METHODS FOR TUNING PARAMETER SELECTION IN ROBUST SPARSE REGRESSION MODELING by

The robust lasso-type regularized regression is a useful tool for simultaneous estimation and variable selection even in the presence of outliers. Crucial issues in the robust modeling procedure include the selection of regularization parameters and also a tuning constant in outlier detection. Although the performance of the robust sparse regression strongly depends on the proper choice of these tuning parameters, little attention was paid for this issue, particularly in the presence of outliers. We consider the problem of choosing the tuning parameters and propose an information-theoretic criterion based on the bootstrap. Although the bootstrap information criterion has several advantages on its flexibility and weak assumptions, a bootstrap sample may contain more outliers compared with those included in the original sample, since the bootstrap sample is drawn randomly. This implies that the bootstrap information criterion may be obtained from the highly contaminated bootstrap sample by outliers, so the resulting criterion may produce biased results. In order to overcome the drawback, we propose a robust bootstrap information criterion via winsorizing technique (Srivastava et al., 2010) in line with the efficient bootstrap information criterion (Konishi and Kitagawa, 1996) for choosing an optimal set of tuning parameters. Monte Carlo simulations and real data analysis are conducted to investigate the effectiveness of the proposed method. We observe that the proposed robust efficient bootstrap information criterion produces reliable model estimates and performs well in the presence of outliers.