Tuning Parameter Selection Based on Blocked $$3\times 2$$ Cross-Validation for High-Dimensional Linear Regression Model

Abstract

In high-dimensional linear regression, selecting an appropriate tuning parameter is essential for the penalized linear models. From the perspective of the expected prediction error of the model, cross-validation methods are commonly used to select the tuning parameter in machine learning. In this paper, blocked \(3\times 2\) cross-validation (\(3\times 2\) BCV) is proposed as the tuning parameter selection method because of its small variance for the prediction error estimation. Under some weaker conditions than leave-\(n_v\)-out cross-validation, the tuning parameter selection method based on \(3\times 2\) BCV is proved to be consistent for the high-dimensional linear regression model. Furthermore, simulated and real data experiments support the theoretical results and demonstrate that the proposed method works well in several criteria about selecting the true model.