A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

Bibliographic Data

ID16912414
AuthorsJin Yuan (0000-0002-5803-6626, Xi'an Jiaotong University), Xianghui Yuan (0000-0003-1466-5268, Xi'an Jiaotong University, corresponding author)
Year2023
Volume13
Issue2
Publication date2023-04-01
Open AccessYes
TypeARTICLE
VenueSAGE Open (JOURNAL)
Journal identifiersISSN: 2158-2440 • E-ISSN: 2158-2440
PublisherSAGE Publications (PUBLISHER • US)
DOI10.1177/21582440231174777
OpenAlexW4379537947
LanguageEN
References cited32

Covariance matrix estimation plays a significant role in both in the theory and practice of portfolio analysis and risk management. This paper deals with the available data prior to developing a factor model to enhance covariance matrix estimation. Our work has two main outcomes. First, for a general linear model with unknown prior parameters, a class of best linear empirical Bayes estimators is established through two kinds of architectures to improve the estimation accuracy by utilizing additional data prior. The theoretical results indicate two key points: the proposed estimators are equivalent to the linear minimum mean-square error estimator when complete or sufficient partial data prior are provided; and the proposed estimators perform better than the optimal weighted least squares method, which ignores the data prior in each situation. Second, the proposed estimators are used for calculating a high-dimensional covariance matrix through factor models. The numerical example and the simulation results verify the effectiveness of our methods

Bayes estimator · Bayes' theorem · Bayesian probability · Covariance · Covariance matrix · Estimation of covariance matrices · Estimator · Linear model · Mathematical optimization · Statistics · Computer Science · Financial Markets and Investment Strategies · Financial Risk and Volatility Modeling · Housing Market and Economics · Mathematics · Applied Mathematics

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