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Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

  • You, Jinhong
  • Zhou, Xian
  • Zhou, Yong
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    We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 5 (May)
    Pages: 1079-1101

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1079-1101
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    1. Breusch, T S & Pagan, A R, 1980. "The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 239-53, January.
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    3. Qi Li & Aman Ullha, 1998. "Estimating partially linear panel data models with one-way error components," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 145-166.
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    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    8. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    9. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
    10. Hong, Sheng-Yan, 2002. "Normal Approximation Rate and Bias Reduction for Data-Driven Kernel Smoothing Estimator in a Semiparametric Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 1-20, January.
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