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

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.