Abstract
We combine the robust criterion with the lasso penalty together for the high-dimensional threshold model. It estimates regression coeffcients as well as the threshold parameter robustly that can be resistant to outliers or heavy-tailed noises and perform variable selection simultaneously. We illustrate our approach with the absolute loss, the Huber’s loss, and the Tukey’s loss, it can also be extended to any other robust losses. Simulation studies are conducted to demonstrate the usefulness of our robust approach. Finally, we use our estimators to investigate the presence of a shift in the effect of debt on future GDP growth.
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The authors appreciate the editor, associate editor and referees for comments that led to the improvements of this paper.
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Supported by the National Natural Science Foundation of China (No.11671349) and the grants from the Key Projects of the National Natural Science Foundation of China (No.11731101).
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Li, Bw., Zhang, Yq. & Tang, Ns. Robust Variable Selection and Estimation in Threshold Regression Model. Acta Math. Appl. Sin. Engl. Ser. 36, 332–346 (2020). https://doi.org/10.1007/s10255-020-0939-y
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DOI: https://doi.org/10.1007/s10255-020-0939-y