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A Cholesky-based estimation for large-dimensional covariance matrices

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  • Xiaoning Kang
  • Chaoping Xie
  • Mingqiu Wang

Abstract

This paper develops a new method to estimate a large-dimensional covariance matrix when the variables have no natural ordering among themselves. The modified Cholesky decomposition technique is used to provide a set of estimates of the covariance matrix under multiple orderings of variables. The proposed estimator is in the form of a linear combination of these available estimates and the identity matrix. It is positive definite and applicable in large dimensions. The merits of the proposed estimator are demonstrated through the numerical study and a real data example by comparison with several existing methods.

Suggested Citation

  • Xiaoning Kang & Chaoping Xie & Mingqiu Wang, 2020. "A Cholesky-based estimation for large-dimensional covariance matrices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 1017-1030, April.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:6:p:1017-1030
    DOI: 10.1080/02664763.2019.1664424
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    Cited by:

    1. Kang, Xiaoning & Wang, Mingqiu, 2021. "Ensemble sparse estimation of covariance structure for exploring genetic disease data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    2. 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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