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Bicluster Analysis of Heterogeneous Panel Data via M-Estimation

Author

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  • Weijie Cui

    (School of Management, University of Science and Technology of China, Hefei 230026, China)

  • Yong Li

    (School of Management, University of Science and Technology of China, Hefei 230026, China
    New Finance Research Center, International Institute of Finance, University of Science and Technology of China, Hefei 230026, China)

Abstract

This paper investigates the latent block structure in the heterogeneous panel data model. It is assumed that the regression coefficients have group structures across individuals and structural breaks over time, where change points can cause changes to the group structures and structural breaks can vary between subgroups. To recover the latent block structure, we propose a robust biclustering approach that utilizes M-estimation and concave fused penalties. An algorithm based on local quadratic approximation is developed to optimize the objective function, which is more compact and efficient than the ADMM algorithm. Moreover, we establish the oracle property of the penalized M-estimators and prove that the proposed estimator recovers the latent block structure with a probability approaching one. Finally, simulation studies on multiple datasets demonstrate the good finite sample performance of the proposed estimators.

Suggested Citation

  • Weijie Cui & Yong Li, 2023. "Bicluster Analysis of Heterogeneous Panel Data via M-Estimation," Mathematics, MDPI, vol. 11(10), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2333-:d:1148679
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    References listed on IDEAS

    as
    1. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    2. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    3. Okui, Ryo & Wang, Wendun, 2021. "Heterogeneous structural breaks in panel data models," Journal of Econometrics, Elsevier, vol. 220(2), pages 447-473.
    4. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage Estimation Of Regression Models With Multiple Structural Changes," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1376-1433, December.
    5. Lumsdaine, Robin L. & Okui, Ryo & Wang, Wendun, 2023. "Estimation of panel group structure models with structural breaks in group memberships and coefficients," Journal of Econometrics, Elsevier, vol. 233(1), pages 45-65.
    6. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    Full references (including those not matched with items on IDEAS)

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