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arXiv · 1802.06048

High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition

Yilei Wu·Yingli Qin·Mu Zhu
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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 L and a diagonal component D. The rank of L 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 blockwise coordinate descent algorithm, which iteratively updates L and D, 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.

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Yilei Wu, Yingli Qin, Mu Zhu. 2018-02-16. High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition. https://arxiv.org/abs/1802.06048

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