The accuracy of response variables is crucially important to train regression models. In some situations, including the high-dimensional case, response observations tend to be inaccurate, which would lead to biased estimators by directly fitting a conventional model. For analyzing data with anomalous responses in the high-dimensional case, in this work, we adopt γ-divergence to conduct variable selection and estimation methods. The proposed method possesses good robustness to anomalous responses, and the proportion of abnormal data does not need to be modeled. It is implemented by an efficient coordinate descent algorithm. In the setting where the dimensionality p can grow exponentially fast with the sample size n, we rigorously establish variable selection consistency and estimation bounds. Numerical simulations and an application on real data are presented to demonstrate the performance of the proposed method.

中文翻译：

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具有异常响应的数据的稳健高维回归

响应变量的准确性对于训练回归模型至关重要。在某些情况下，包括高维情况，响应观察往往是不准确的，这会导致通过直接拟合传统模型导致估计量有偏差。为了分析高维情况下具有异常响应的数据，在这项工作中，我们采用γ-散度进行变量选择和估计方法。该方法对异常响应具有良好的鲁棒性，不需要对异常数据的比例进行建模。它由有效的坐标下降算法实现。在维数 p 可以随着样本大小 n 呈指数级快速增长的情况下，我们严格建立了变量选择一致性和估计界限。