James–Stein for the leading eigenvector

Lisa R Goldberg and Alec N Kercheval

Department of Economics, Working Paper Series from Department of Economics, Institute for Business and Economic Research, UC Berkeley

Abstract: Recent research 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. We show 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. We describe a data-driven eigenvector shrinkage estimator in the HL regime called "James-Stein for eigenvectors" (JSE) and its close relationship with the James-Stein (JS) estimator for a collection of averages. We show, both theoretically and with numerical experiments, that, for certain variance-minimizing problems of practical importance, efforts to correct eigenvalues have little value in comparison to the JSE correction of the leading eigenvector. When certain extra information is present, JSE is a consistent estimator of the leading eigenvector.

Keywords: Bias; Sample Size; asymptotic regime; shrinkage; factor model; optimization; covariance matrix (search for similar items in EconPapers)
Date: 2023-01-10
New Economics Papers: this item is included in nep-ecm
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