We construct confidence regions in high dimensions by inverting the globaltest statistics, and use them to choose the tuning parameter for penalized regression. The selected model corresponds to the point in the confidence region of the parameters that minimizes the penalty, making it the least complex model that still has acceptable fit according to the test that defines the confidence region. As the globaltest is particularly powerful in the presence of many weak predictors, it connects well to ridge regression, and we thus focus on ridge penalties in this paper. The confidence region method is quick to calculate, intuitive, and gives decent predictive potential. As a tuning parameter selection method it may even outperform classical methods such as cross-validation in terms of mean squared error of prediction, especially when the signal is weak. We illustrate the method for linear models in simulation study and for Cox models in real gene expression data of breast cancer samples.

中文翻译：

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Globaltest 置信区域及其在岭回归中的应用

我们通过反转全局测试统计量来构建高维度的置信区域，并使用它们来选择惩罚回归的调整参数。所选模型对应于参数置信区域中使惩罚最小化的点，使其成为根据定义置信区域的测试仍然具有可接受拟合的最简单的模型。由于 globaltest 在存在许多弱预测器的情况下特别强大，因此它与岭回归有很好的联系，因此我们在本文中关注岭惩罚。置信区域方法计算快速、直观，并提供了不错的预测潜力。作为一种调整参数选择方法，它甚至可能在预测的均方误差方面优于交叉验证等经典方法，尤其是在信号较弱的情况下。