In the context of the high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where we propose to control predictive risk and False Discovery Rate simultaneously. For this purpose, we obtain a convenient trade-off thanks to a proper calibration of the hyperparameter K appearing in the penalty function. We obtain non-asymptotic theoretical bounds on the False Discovery Rate with respect to K. We then provide an algorithm for the calibration of K. It is based on completely observable quantities in view of applications. Our algorithm is validated by an extensive simulation study.

翻译：在有序变量的高维高斯线性回归背景下，我们通过最小化惩罚最小二乘准则研究了变量选择过程。我们聚焦于模型选择，目标是同时控制预测风险与错误发现率。为此，通过对惩罚函数中的超参数K进行恰当校准，我们实现了有效的权衡。我们得到了关于K的非渐近理论界，用于界定错误发现率。随后，我们提出了一种基于完全可观测量的K校准算法，以便应用于实际场景。该算法通过广泛的模拟研究得到验证。