James-Stein Estimator of leading eigenvectors of large volatility matrix and its effect on portfolio optimization resentation

Oregon Convention Center 

Recently, a James-Stein shrinkage (JS) estimator has gained attention as a powerful tool for estimating the leading eigenvector of covariance matrices. The efficacy of the JS estimator has been demonstrated under a strongly-spiked leading eigenvalue model, using the high-dimensional, low-sample-size (HDLSS) asymptotic regime, where the number of variables increases while the sample size remains fixed. In this work, we extend the application of the JS shrinkage to the regime of moderately-spiked leading eigenvalues, and reveal a key condition, involving a signal-to-noise ratio, for the JS estimator to be useful. Furthermore, we develop shrinkage estimators for principal component variance and scores, enabling their application in high-dimensional principal component analysis. The implication of the work in Markowitz's mean-variance optimal portfolio will be discussed as well.