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Semiparametric Regression with Kernel Error Model

Author

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  • Ao Yuan

    (Howard University)

  • Jan G. De Gooijer

    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

Abstract

We propose and study a class of regression models, in which the mean function is specified parametrically as in the existing regression methods, but the residual distribution is modeled nonparametrically by a kernel estimator, without imposing any assumption on its distribution. This specification is different from the existing semiparametric regression models. The asymptotic properties of such likelihood and the maximum likelihood estimate (MLE) under this semiparametric model are studied. We show that under some regularity conditions, the MLE under this model is consistent (as compared to the possibly pseudo consistency of the parameter estimation under the existing parametric regression model), and is asymptotically normal with rate sqrt{n} and efficient. The nonparametric pseudo-likelihood ratio has the Wilks property as the true likelihood ratio does. Simulated examples are presented to evaluate the accuracy of the proposed semiparametric MLE method.

Suggested Citation

  • Ao Yuan & Jan G. De Gooijer, 2006. "Semiparametric Regression with Kernel Error Model," Tinbergen Institute Discussion Papers 06-058/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20060058
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    References listed on IDEAS

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    1. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
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    7. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
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    Citations

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    Cited by:

    1. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    2. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    3. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    4. Yao, Weixin, 2013. "A note on EM algorithm for mixture models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 519-526.
    5. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    6. Zhang, Xibin & King, Maxwell L. & Shang, Han Lin, 2014. "A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 218-234.
    7. McCloud, Nadine & Parmeter, Christopher F., 2020. "Determining the Number of Effective Parameters in Kernel Density Estimation," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    8. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2011. "Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 10/11, Monash University, Department of Econometrics and Business Statistics.
    9. Guohua Feng & Chuan Wang & Xibin Zhang, 2019. "Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach," Journal of Productivity Analysis, Springer, vol. 51(1), pages 1-19, February.
    10. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    11. Jan G. De Gooijer & Ao Yuan, 2008. "MDL Mean Function Selection in Semiparametric Kernel Regression Models," Tinbergen Institute Discussion Papers 08-046/4, Tinbergen Institute.
    12. Zhang, Jun & Lin, Bingqing & Zhou, Yan, 2021. "Kernel density estimation for partial linear multivariate responses models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    13. Chee, Chew-Seng & Seo, Byungtae, 2020. "Semiparametric estimation for linear regression with symmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    14. De Gooijer, Jan G. & Reichardt, Hugo, 2021. "A multi-step kernel–based regression estimator that adapts to error distributions of unknown form," LSE Research Online Documents on Economics 115083, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    information bound; kernel density estimator; maximum likelihood estimate; nonlinear regression; semiparametric model; U-statistic; Wilks property;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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