Regularizing stock return covariance matrices via multiple testing of correlations
提出一种大规模推断方法，通过多重检验将不显著的相关性设为零，再结合收缩估计，得到稀疏且正定的协方差矩阵，在模拟和真实投资组合优化中表现优于其他方法。
This paper develops a large-scale inference approach for the regularization\nof stock return covariance matrices. The framework allows for the presence of\nheavy tails and multivariate GARCH-type effects of unknown form among the stock\nreturns. The approach involves simultaneous testing of all pairwise\ncorrelations, followed by setting non-statistically significant elements to\nzero. This adaptive thresholding is achieved through sign-based Monte Carlo\nresampling within multiple testing procedures, controlling either the\ntraditional familywise error rate, a generalized familywise error rate, or the\nfalse discovery proportion. Subsequent shrinkage ensures that the final\ncovariance matrix estimate is positive definite and well-conditioned while\npreserving the achieved sparsity. Compared to alternative estimators, this new\nregularization method demonstrates strong performance in simulation experiments\nand real portfolio optimization.\n