In high-dimensional linear regression, the dimension of variables is always greater than the sample size. In this situation, the traditional variance estimation technique based on ordinary least squares constantly exhibits a high bias even under sparsity assumption. One of the major reasons is the high spurious correlation between unobserved realized noise and several predictors. To alleviate this problem, a refitted cross-validation (RCV) method has been proposed in the literature. However, for a complicated model, the RCV exhibits a lower probability that the selected model includes the true model in case of finite samples. This phenomenon may easily result in a large bias of variance estimation. Thus, a model selection method based on the ranks of the frequency of occurrences in six votes from a blocked 3×2 cross-validation is proposed in this study. The proposed method has a considerably larger probability of including the true model in practice than the RCV method. The variance estimation obtained using the model selected by the proposed method also shows a lower bias and a smaller variance. Furthermore, theoretical analysis proves the asymptotic normality property of the proposed variance estimation.

在高维线性回归中，变量的维数总是大于样本量。在这种情况下，即使在稀疏假设下，基于普通最小二乘的传统方差估计技术也不断表现出高偏差。主要原因之一是未观察到的已实现噪声与几个预测变量之间的高虚假相关性。为了缓解这个问题，文献中提出了一种改装交叉验证（RCV）方法。然而，对于一个复杂的模型，在有限样本的情况下，RCV 显示出所选模型包含真实模型的较低概率。这种现象很容易导致方差估计的偏差很大。因此，本研究提出了一种基于阻塞的 3×2 交叉验证中 6 票出现频率等级的模型选择方法。与 RCV 方法相比，所提出的方法在实践中包含真实模型的概率要大得多。使用该方法选择的模型获得的方差估计也显示出较低的偏差和较小的方差。此外，理论分析证明了所提出的方差估计的渐近正态性。