For high‐dimensional data, the standard empirical estimator for the covariance matrix is very poor, and thus many methods have been proposed to more accurately estimate the covariance structure of high‐dimensional data. In this article, we consider estimation under the assumption of sparsity but regularize with respect to the individual false‐positive rate for incorrectly including a matrix entry in the support of the final estimator. The two benefits of this approach are (1) an interpretable regularization parameter removing the need for computationally expensive tuning and (2) extremely fast computation time arising from use of a binary search algorithm implemented to find the best estimator within a carefully constructed operator norm ball. We compare our approach to universal thresholding estimators and lasso‐style penalized estimators on both simulated data and data from gene expression for cancerous tumours.

中文翻译：

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高维稀疏协方差矩阵的非渐近支持恢复

对于高维数据，协方差矩阵的标准经验估计值非常差，因此提出了许多方法来更准确地估计高维数据的协方差结构。在本文中，我们考虑在稀疏性假设下进行估计，但针对单个假阳性率进行正则化，以在最终估计器的支持下错误地包括矩阵项。这种方法的两个好处是：（1）可解释的正则化参数消除了对计算量大的调整的需要；（2）使用二进制搜索算法以在精心构造的算子范数球中找到最佳估计量而产生的计算时间极快。