The paper presents a method for regularizing large covariance matrices by thresholding, which is shown to be consistent in the operator norm under certain conditions. The method is permutation-invariant and applicable to a wide range of data types, including those with no inherent ordering. The thresholding estimator is compared to other covariance estimation techniques such as banding and shrinkage, and it is shown to perform well in simulations and on climate data. The paper also discusses a cross-validation approach for selecting the threshold and provides theoretical justification for its effectiveness. The results demonstrate that thresholding can achieve good performance in high-dimensional settings, particularly when the true covariance matrix is sparse. The method is applied to climate data, where it successfully identifies distinct spatial patterns corresponding to different regions. The paper concludes with a discussion of the implications of the results for covariance estimation in high-dimensional settings.The paper presents a method for regularizing large covariance matrices by thresholding, which is shown to be consistent in the operator norm under certain conditions. The method is permutation-invariant and applicable to a wide range of data types, including those with no inherent ordering. The thresholding estimator is compared to other covariance estimation techniques such as banding and shrinkage, and it is shown to perform well in simulations and on climate data. The paper also discusses a cross-validation approach for selecting the threshold and provides theoretical justification for its effectiveness. The results demonstrate that thresholding can achieve good performance in high-dimensional settings, particularly when the true covariance matrix is sparse. The method is applied to climate data, where it successfully identifies distinct spatial patterns corresponding to different regions. The paper concludes with a discussion of the implications of the results for covariance estimation in high-dimensional settings.