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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
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    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.

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    Bibliographic Info

    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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    Related research

    Keywords: Asymptotic normality Heteroscedasticity One-way error component structure Panel data Partially linear model Semiparametric estimation;

    References

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    1. 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.
    2. Zongwu Cai & Jianqing Fan & Qiwei Yao, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    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.
    4. Breusch, T.S. & Pagan, A.R., . "The Lagrange multiplier test and its applications to model specification in econometrics," CORE Discussion Papers RP -412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. 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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    8. Li, Qi & Stengos, Thanasis, 1994. "Adaptive Estimation in the Panel Data Error Component Model with Heteroskedasticity of Unknown Form," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(4), pages 981-1000, November.
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    10. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying-coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80.
    11. Gao, Jiti, 1995. "The laws of the iterated logarithm of some estimates in partly linear models," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 153-162, November.
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    Cited by:
    1. 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, vol. 98(2), pages 165-195, April.

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