Review Articles

Cholesky-based model averaging for covariance matrix estimation

Hao Zheng ,

Gilead Sciences, Inc., Foster City, CA, USA

Kam-Wah Tsui ,

Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA

Xiaoning Kang ,

International Business College, Dongbei University of Finance and Economics, Dalian, China

Xinwei Deng

Department of Statistics, Virginia Tech, Blacksburg, VA, USA

Pages 48-58 | Received 01 Mar. 2017, Accepted 29 May. 2017, Published online: 28 Jul. 2017,
  • Abstract
  • Full Article
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Estimation of large covariance matrices is of great importance in multivariate analysis. The modified Cholesky decomposition is a commonly used technique in covariance matrix estimation given a specific order of variables. However, information on the order of variables is often unknown, or cannot be reasonably assumed in practice. In this work, we propose a Cholesky-based model averaging approach of covariance matrix estimation for high dimensional data with proper regularisation imposed on the Cholesky factor matrix. The proposed method not only guarantees the positive definiteness of the covariance matrix estimate, but also is applicable in general situations without the order of variables being pre-specified. Numerical simulations are conducted to evaluate the performance of the proposed method in comparison with several other covariance matrix estimates. The advantage of our proposed method is further illustrated by a real case study of equity portfolio allocation.

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