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Nonparametric regression estimation with general parametric error covariance

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  • Martins-Filho, Carlos
  • Yao, Feng

Abstract

The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the error covariance matrix is proposed. Sufficient conditions for its asymptotic normality are given and its efficiency relative to the local linear estimator is established. We give examples of how our results are useful in some recently studied regression models. A Monte Carlo study confirms the asymptotic theory predictions and compares our estimator with some recently proposed alternative estimation procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:309-333
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    8. 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.
    9. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    10. Ke Yang, 2012. "Multivariate Local Polynomial Regression With Autocorrelated Errors," Economics Bulletin, AccessEcon, vol. 32(4), pages 3298-3305.
    11. Christopher F. Parmeter & Jeffrey S. Racine, 2018. "Nonparametric Estimation and Inference for Panel Data Models," Department of Economics Working Papers 2018-02, McMaster University.
    12. Eduardo A. Souza-Rodrigues, 2016. "Nonparametric Regression with Common Shocks," Econometrics, MDPI, vol. 4(3), pages 1-17, September.
    13. Ke Yang, 2013. "An Improved Local-linear Estimator For Nonparametric Regression With Autoregressive Errors," Economics Bulletin, AccessEcon, vol. 33(1), pages 19-27.
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