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Estimation and Simultaneous Confidence Bands for Fixed-Effects Panel Data Partially Linear Models

Author

Listed:
  • Suigen Yang

    (College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China)

  • Xiujuan Yang

    (IT Department, China Southern Airlines, Guangzhou 510405, China)

  • Xuefei Wang

    (School of Statistics, Beijing Normal University, Beijing 100875, China)

Abstract

In this paper, we study the estimation and simultaneous confidence band (SCB) problems for fixed-effects panel data partially linear models. We remove the fixed effects and then obtain estimators for the parametric and nonparametric components, which do not depend on the fixed effects. We establish the asymptotic distribution of the maximum absolute deviation between the estimated nonparametric component and the true nonparametric component under some suitable conditions; hence, this result can be used to construct the simultaneous confidence band for the nonparametric component. Based on the asymptotic distribution, it becomes difficult to construct the simultaneous confidence band. The reason for this is that the asymptotic distribution involves estimators of the asymptotic bias and conditional variance, as well as the choice of bandwidth for estimating the second derivative of the nonparametric function. Clearly, this will result in a computational burden and accumulated errors. To overcome these problems, we propose a bootstrap method to construct the simultaneous confidence band. The Monte Carlo results indicate that the proposed bootstrap method exhibits better performance with limited samples. An empirical application is presented to evaluate the performance of the proposed method.

Suggested Citation

  • Suigen Yang & Xiujuan Yang & Xuefei Wang, 2024. "Estimation and Simultaneous Confidence Bands for Fixed-Effects Panel Data Partially Linear Models," Mathematics, MDPI, vol. 12(23), pages 1-18, November.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3774-:d:1533181
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    References listed on IDEAS

    as
    1. De Vos, Ignace & Stauskas, Ovidijus, 2024. "Cross-section bootstrap for CCE regressions," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Henderson, Daniel J. & Ullah, Aman, 2005. "A nonparametric random effects estimator," Economics Letters, Elsevier, vol. 88(3), pages 403-407, September.
    3. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 928-955, November.
    4. Li, Gaorong & Peng, Heng & Tong, Tiejun, 2013. "Simultaneous confidence band for nonparametric fixed effects panel data models," Economics Letters, Elsevier, vol. 119(3), pages 229-232.
    5. Zhang, Junhua & Feng, Sanying & Li, Gaorong & Lian, Heng, 2011. "Empirical likelihood inference for partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 113(2), pages 165-167.
    6. Sanying Feng & Gaorong Li & Tiejun Tong & Shuanghua Luo, 2020. "Testing for heteroskedasticity in two-way fixed effects panel data models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(1), pages 91-116, January.
    7. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
    8. Yiguo Sun & Raymond J. Carroll & Dingding Li, 2009. "Semiparametric estimation of fixed-effects panel data varying coefficient models," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 101-129, Emerald Group Publishing Limited.
    9. Nicolai Bissantz & Lutz Dümbgen & Hajo Holzmann & Axel Munk, 2007. "Non‐parametric confidence bands in deconvolution density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 483-506, June.
    10. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.
    11. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    12. Li, Qi, 1996. "On the root-N-consistent semiparametric estimation of partially linear models," Economics Letters, Elsevier, vol. 51(3), pages 277-285, June.
    13. Bissantz, Nicolai & Dümbgen, Lutz & Holzmann, Hajo & Munk, Axel, 2007. "Nonparametric confidence bands in deconvolution density estimation," Technical Reports 2007,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    15. Hsiao,Cheng, 2022. "Analysis of Panel Data," Cambridge Books, Cambridge University Press, number 9781009060752, November.
    16. Hsiao,Cheng, 2022. "Analysis of Panel Data," Cambridge Books, Cambridge University Press, number 9781316512104, November.
    17. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Semiparametric estimation of fixed effects panel data single-index model," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1595-1602.
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