A theoretical study of Stein's covariance estimator
研究了Stein提出的协方差估计量，发现未等渗化时风险降低有限，等渗化后风险显著降低，并识别出三种行为模式。
Stein proposed an estimator to address the poor performance of the sample covariance matrix for samples of small size. The estimator does not impose sparsity conditions and uses an isotonizing algorithm to preserve the order of the sample eigenvalues. Despite its superior numerical performance, its theoretical properties are not well understood. We demonstrate that Stein's covariance estimator gives modest risk reductions when it is not isotonized, and when it is isotonized the risk reductions are significant. Three broad regimes of the estimator's behaviour are identified.