Portfolio managers faced with limited sample sizes must use factor models to\nestimate the covariance matrix of a high-dimensional returns vector. For the\nsimplest one-factor market model, success rests on the quality of the estimated\nleading eigenvector "beta".\n When only the returns themselves are observed, the practitioner has available\nthe "PCA" estimate equal to the leading eigenvector of the sample covariance\nmatrix. This estimator performs poorly in various ways. To address this problem\nin the high-dimension, limited sample size asymptotic regime and in the context\nof estimating the minimum variance portfolio, Goldberg, Papanicolau, and\nShkolnik developed a shrinkage method (the "GPS estimator") that improves the\nPCA estimator of beta by shrinking it toward a constant target unit vector.\n In this paper we continue their work to develop a more general framework of\nshrinkage targets that allows the practitioner to make use of further\ninformation to improve the estimator. Examples include sector separation of\nstock betas, and recent information from prior estimates. We prove some precise\nstatements and illustrate the resulting improvements over the GPS estimator\nwith some numerical experiments.\n