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Covariance Regression Analysis

Author

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  • Tao Zou
  • Wei Lan
  • Hansheng Wang
  • Chih-Ling Tsai

Abstract

This article introduces covariance regression analysis for a p-dimensional response vector. The proposed method explores the regression relationship between the p-dimensional covariance matrix and auxiliary information. We study three types of estimators: maximum likelihood, ordinary least squares, and feasible generalized least squares estimators. Then, we demonstrate that these regression estimators are consistent and asymptotically normal. Furthermore, we obtain the high dimensional and large sample properties of the corresponding covariance matrix estimators. Simulation experiments are presented to demonstrate the performance of both regression and covariance matrix estimates. An example is analyzed from the Chinese stock market to illustrate the usefulness of the proposed covariance regression model. Supplementary materials for this article are available online.

Suggested Citation

  • Tao Zou & Wei Lan & Hansheng Wang & Chih-Ling Tsai, 2017. "Covariance Regression Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 266-281, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:266-281
    DOI: 10.1080/01621459.2015.1131699
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    Citations

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    Cited by:

    1. Zhu, Xuening & Wang, Weining & Wang, Hansheng & Härdle, Wolfgang Karl, 2019. "Network quantile autoregression," Journal of Econometrics, Elsevier, vol. 212(1), pages 345-358.
    2. Guanyu Hu & Ming-Hui Chen & Nalini Ravishanker, 2023. "Bayesian analysis of spherically parameterized dynamic multivariate stochastic volatility models," Computational Statistics, Springer, vol. 38(2), pages 845-869, June.
    3. Wu, Shihao & Li, Zhe & Zhu, Xuening, 2023. "A distributed community detection algorithm for large scale networks under stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Li Guo & Wolfgang Karl Härdle & Yubo Tao, 2024. "A Time-Varying Network for Cryptocurrencies," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 437-456, April.
    5. Zou, Tao & Lan, Wei & Li, Runze & Tsai, Chih-Ling, 2022. "Inference on covariance-mean regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 318-338.
    6. Yang, Yuehan & Xia, Siwei & Yang, Hu, 2023. "Multivariate sparse Laplacian shrinkage for joint estimation of two graphical structures," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    7. Ren, Yimeng & Li, Zhe & Zhu, Xuening & Gao, Yuan & Wang, Hansheng, 2024. "Distributed estimation and inference for spatial autoregression model with large scale networks," Journal of Econometrics, Elsevier, vol. 238(2).
    8. Chen, Elynn Y. & Fan, Jianqing & Zhu, Xuening, 2023. "Community network auto-regression for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1239-1256.
    9. Zhu, Xuening & Chang, Xiangyu & Li, Runze & Wang, Hansheng, 2019. "Portal nodes screening for large scale social networks," Journal of Econometrics, Elsevier, vol. 209(2), pages 145-157.
    10. Guanyu Hu & Yishu Xue & Zhihua Ma, 2020. "Bayesian Clustered Coefficients Regression with Auxiliary Covariates Assistant Random Effects," Papers 2004.12022, arXiv.org, revised Aug 2021.

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