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.

中文翻译：

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阈值回归模型中的稳健变量选择和估计

对于高维阈值模型，我们将鲁棒标准与套索惩罚结合在一起。它可以稳健地估计回归系数以及阈值参数，可以抵抗异常值或重尾噪声并同时执行变量选择。我们用绝对损失、Huber 损失和 Tukey 损失来说明我们的方法，它也可以扩展到任何其他稳健损失。进行模拟研究以证明我们稳健方法的有用性。最后，我们使用我们的估计量来调查债务对未来 GDP 增长的影响是否存在转变。