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

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  • You, Jinhong
  • Zhou, Xian
  • Zhou, Yong

Abstract

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.

Suggested Citation

  • You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1079-1101
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    Cited by:

    1. Jianhong Shi & Fanrong Zhao, 2018. "Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition," Statistical Papers, Springer, vol. 59(2), pages 487-511, June.
    2. Rodriguez-Poo, Juan M. & Soberón, Alexandra, 2015. "Nonparametric estimation of fixed effects panel data varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 95-122.
    3. Jing-Jing Zhang & Han-Ying Liang & Amei Amei, 2014. "Asymptotic normality of estimators in heteroscedastic errors-in-variables model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 165-195, April.
    4. Hu, Jianhua & You, Jinhong & Zhou, Xian, 2017. "Improved estimation of fixed effects panel data partially linear models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 96-111.

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