James-Stein estimation of the first principal component

The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that sample mean, classically regarded as usual estimator, may be suboptimal dimensions. development James-Stein addresses this paradox, by now inspired a large literature on theme shrinkage In direction, we develop type estimator for first principal component dimension and low size data set. shrinks eigenvector covariance matrix under spiked model, yields superior asymptotic guarantees. Our derivation draws close connection to original formula so motivation recipe is intuited natural way.