Covariance Estimation for Wide Data

ABSTRACT Reliable estimation of the covariance matrix is fundamental to multivariate analysis, second in importance only to the mean. Its accuracy directly impacts applications in economics, finance, chemistry, health science, bioinformatics, climate research, signal processing, and social network analysis. Modern data environments often involve wide data, where the number of variables is comparable to or exceeds the number of observations, making classical estimators unstable or singular. This review synthesizes recent advances in high‐dimensional covariance estimation, focusing on thresholding procedures, linear and nonlinear shrinkage methods, graphical model‐based approaches, and estimation techniques using random matrix theory. A unifying taxonomy is proposed that organizes these diverse techniques under a single conceptual framework, highlighting their interconnections and guiding the selection of appropriate estimators in wide‐data settings.