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James-Stein for the leading eigenvector
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DOI：10.1073/pnas.2207046120.png)
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摘要
En 中文
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.
Keyword:
asymptotic regime
shrinkage
factor model
optimization
covariance matrix
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9.1
论文数:
10.8W
被引数:
73.5W
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