In this paper, we consider prediction and variable selection in the misspecified binary classification models under the high-dimensional scenario. We focus on two approaches to classification, which are computationally efficient, but lead to model misspecification. The first one is to apply penalized logistic regression to the classification data, which possibly do not follow the logistic model. The second method is even more radical: we just treat class labels of objects as they were numbers and apply penalized linear regression. In this paper, we investigate thoroughly these two approaches and provide conditions, which guarantee that they are successful in prediction and variable selection. Our results hold even if the number of predictors is much larger than the sample size. The paper is completed by the experimental results.

中文翻译：

---

高维错误指定二元分类中的预测和变量选择

在本文中，我们考虑了高维场景下错误指定的二元分类模型中的预测和变量选择。我们专注于两种分类方法，它们在计算上是有效的，但会导致模型指定错误。第一个是对可能不遵循逻辑模型的分类数据应用惩罚逻辑回归。第二种方法更加激进：我们只是将对象的类标签视为数字并应用惩罚线性回归。在本文中，我们彻底研究了这两种方法并提供了条件，以保证它们在预测和变量选择方面是成功的。即使预测变量的数量远大于样本量，我们的结果也成立。论文根据实验结果完成。