High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition |
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Authors: | Yilei Wu Yingli Qin Mu Zhu |
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Affiliation: | Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada, N2L 3G1 |
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Abstract: | We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component and a diagonal component . The rank of can either be chosen to be small or controlled by a penalty function. Under moderate conditions on the population covariance/precision matrix itself and on the penalty function, we prove some consistency results for our estimators. A block-wise coordinate descent algorithm, which iteratively updates and , is then proposed to obtain the estimator in practice. Finally, various numerical experiments are presented; using simulated data, we show that our estimator performs quite well in terms of the Kullback–Leibler loss; using stock return data, we show that our method can be applied to obtain enhanced solutions to the Markowitz portfolio selection problem. The Canadian Journal of Statistics 48: 308–337; 2020 © 2019 Statistical Society of Canada |
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Keywords: | Akaike information criterion consistency coordinate descent eigen-decomposition Kullback–Leibler loss log-determinant semi-definite programming Markowitz portfolio selection |
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