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Nonparametric regression estimation with general parametric error covariance: a more efficient two-step estimator

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  • Liangjun Su
  • Aman Ullah
  • Yun Wang

Abstract

Recently Martins-Filho and Yao (J Multivar Anal 100:309–333, 2009 ) have proposed a two-step estimator of nonparametric regression function with parametric error covariance and demonstrate that it is more efficient than the usual LLE. In the present paper we demonstrate that MY’s estimator can be further improved. First, we extend MY’s estimator to the multivariate case, and also establish the asymptotic theorem for the slope estimators; second, we propose a more efficient two-step estimator for nonparametric regression function with general parametric error covariance, and develop the corresponding asymptotic theorems. Monte Carlo study shows the relative efficiency loss of MY’s estimator in comparison with our estimator in nonparametric regression with either AR(2) errors or heteroskedastic errors. Finally, in an empirical study we apply the proposed estimator to estimate the public capital productivity to illustrate its performance in a real data setting. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Liangjun Su & Aman Ullah & Yun Wang, 2013. "Nonparametric regression estimation with general parametric error covariance: a more efficient two-step estimator," Empirical Economics, Springer, vol. 45(2), pages 1009-1024, October.
    • Handle: RePEc:spr:empeco:v:45:y:2013:i:2:p:1009-1024
    DOI: 10.1007/s00181-012-0641-x
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    References listed on IDEAS

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    1. Su, Liangjun & Ullah, Aman, 2006. "More Efficient Estimation In Nonparametric Regression With Nonparametric Autocorrelated Errors," Econometric Theory, Cambridge University Press, vol. 22(1), pages 98-126, February.
    2. Martins-Filho, Carlos & Yao, Feng, 2009. "Nonparametric regression estimation with general parametric error covariance," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 309-333, March.
    3. Holtz-Eakin, Douglas, 1994. "Public-Sector Capital and the Productivity Puzzle," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 12-21, February.
    4. Linton, Oliver B. & Mammen, Enno, 2008. "Nonparametric transformation to white noise," Journal of Econometrics, Elsevier, vol. 142(1), pages 241-264, January.
    5. Su, Liangjun & Ullah, Aman, 2007. "More efficient estimation of nonparametric panel data models with random effects," Economics Letters, Elsevier, vol. 96(3), pages 375-380, September.
    6. Xiao Z. & Linton O.B. & Carroll R.J. & Mammen E., 2003. "More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 980-992, January.
    7. Evans, Paul & Karras, Georgios, 1994. "Are Government Activities Productive? Evidence from a Panel of U.S. States," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 1-11, February.
    8. Leah M. Cook & Alicia H. Munnell, 1990. "How does public infrastructure affect regional economic performance?," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 11-33.
    9. Baltagi, Badi H & Pinnoi, Nat, 1995. "Public Capital Stock and State Productivity Growth: Further Evidence from an Error Components Model," Empirical Economics, Springer, vol. 20(2), pages 351-359.
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    Cited by:

    1. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    2. Huang, Bai & Lee, Tae-Hwy & Ullah, Aman, 2020. "Combined estimation of semiparametric panel data models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 30-45.
    3. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    4. Artem Prokhorov & Kien C. Tran & Mike G. Tsionas, 2021. "Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors," Empirical Economics, Springer, vol. 60(6), pages 3043-3068, June.
    5. Shujie Ma & Jeffrey S. Racine & Aman Ullah, 2015. "Nonparametric Regression-Spline Random Effects Models," Department of Economics Working Papers 2015-10, McMaster University.
    6. Syed F. Mahmud & Murat Tiniç, 2018. "Herding in Chinese stock markets: a nonparametric approach," Empirical Economics, Springer, vol. 55(2), pages 679-711, September.

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    More about this item

    Keywords

    Covariance matrix; Local linear estimation; Productivity; Relative efficiency; C1; C14; C33;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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