A1227
Title: James-Stein for eigenvectors with applications to constrained optimization
Authors: Lisa Goldberg - University of California, Berkeley (United States) [presenting]
Alec Kercheval - Florida State University (United States)
Hubeyb Gurdogan - University of California, Berkeley (United States)
Abstract: A recipe for estimating covariance matrices tailored to constrained optimization problems is provided, resulting in optimized portfolios with low variance. The recipe relies on recent research that identifies and corrects bias, such as excess dispersion, in the leading sample eigenvector of a factor-based covariance matrix estimated from a high-dimension low sample size (HL) data set. It is shown that eigenvector bias can have a substantial impact on variance-minimizing optimization in the HL regime, while bias in estimated eigenvalues may have little effect. The estimated covariance matrix is obtained with a data-driven eigenvector shrinkage operator called JamesStein for eigenvectors (JSE), which corrects bias that is selectively distorted by constrained optimization. The shrinkage operator is named to emphasize its profound parallels to classical JamesStein (JS) shrinkage operators for a collection of averages.
