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首页> 外文期刊>Journal of applied statistics >Variance estimation based on blocked 3×2 cross-validation in high-dimensional linear regression
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Variance estimation based on blocked 3×2 cross-validation in high-dimensional linear regression

机译：基于阻塞3×2交叉验证的方差估计在高维线性回归中的交叉验证

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摘要

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 3x2 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.
机译：在高维线性回归中，变量的尺寸总是大于样本大小。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常常呈现高偏差。其中一个主要原因是未观察到的实现噪声与几个预测因子之间的高杂散相关性。为了减轻这个问题，在文献中提出了一种改进的交叉验证（RCV）方法。然而，对于复杂的模型，RCV表现出较低的概率，即所选择的模型包括在有限样本的情况下的真实模型。这种现象可以容易地导致方差估计的大偏差。因此，在本研究中提出了一种基于来自封锁的3x2交叉验证的六票票频率的频率的模型选择方法。该方法在实践中具有比RCV方法在实践中具有相当大的概率。使用由所提出的方法选择的模型获得的方差估计也显示了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常态性质。

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