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

翻译：面临抽样规模有限的组合管理者必须使用要素模型来估计高维返回矢量的共变矩阵。 对于简单的单一因素市场模型来说,成功与否取决于估计的先导元体“贝塔”的质量。 当只观察到返回本身时, 执业者可以得到“ PCA” 估计值, 相当于样本共差矩阵的先导源体。 这个估测器在各种方面表现不佳。 要在高差异、 样本规模有限、 吸收系统以及估计最小差异组合的范围内解决这个问题, Goldberg、 Papannicolau 和 Shkolnik 开发了一个缩缩缩方法( “ GPS 估测器 ” ), 通过向恒定目标矢量器缩小, 来改善五氯苯甲醚的天花估计值。 在本文中,我们继续努力开发一个更一般的缩放目标框架, 使执业者能够使用进一步的信息来改进估量器。 例如, 股票贝特的分区分离, 以及最近的一些信息来自先前的估算。 我们用一些精确的说明, 并用数字实验来说明导致GPS 的改进。