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Cholesky-based model averaging for covariance matrix estimation

Author

Listed:
  • Hao Zheng
  • Kam-Wah Tsui
  • Xiaoning Kang
  • Xinwei Deng

Abstract

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.

Suggested Citation

  • Hao Zheng & Kam-Wah Tsui & Xiaoning Kang & Xinwei Deng, 2017. "Cholesky-based model averaging for covariance matrix estimation," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 48-58, January.
    • Handle: RePEc:taf:tstfxx:v:1:y:2017:i:1:p:48-58
    DOI: 10.1080/24754269.2017.1336831
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    Citations

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    Cited by:

    1. Liang, Wanfeng & Ma, Xiaoyan, 2024. "A new approach for ultrahigh-dimensional covariance matrix estimation," Statistics & Probability Letters, Elsevier, vol. 204(C).
    2. Gao, Zhenguo & Wang, Xinye & Kang, Xiaoning, 2023. "Ensemble LDA via the modified Cholesky decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    3. Yuan, Chaoxia & Fang, Fang & Ni, Lyu, 2022. "Mallows model averaging with effective model size in fragmentary data prediction," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    4. Fang, Fang & Yang, Qiwei & Tian, Wenling, 2022. "Cross-validation for selecting the penalty factor in least squares model averaging," Economics Letters, Elsevier, vol. 217(C).
    5. Kang, Xiaoning & Wang, Mingqiu, 2021. "Ensemble sparse estimation of covariance structure for exploring genetic disease data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    6. Bruno P. C. Levy & Hedibert F. Lopes, 2021. "Dynamic Ordering Learning in Multivariate Forecasting," Papers 2101.04164, arXiv.org, revised Nov 2021.

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