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A nonparametric regression estimator that adapts to error distribution of unknown form

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  • Linton, Oliver Bruce
  • Xiao, Zhijie

Abstract

We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our estimator is asymptotically equivalent to the infeasible local maximum likelihood estimator [Staniswalis (1989)], and hence improves on standard kernel estimators when the error distribution is not normal. We investigate the finite sample performance of our procedure on simulated data.

Suggested Citation

  • Linton, Oliver Bruce & Xiao, Zhijie, 2001. "A nonparametric regression estimator that adapts to error distribution of unknown form," SFB 373 Discussion Papers 2001,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200133
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    Cited by:

    1. Wang, Dong, 2010. "Modeling epigenetic modifications under multiple treatment conditions," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1179-1189, April.
    2. 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.
    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. 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.
    6. McCloud, Nadine & Parmeter, Christopher F., 2020. "Determining the Number of Effective Parameters in Kernel Density Estimation," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    7. Moradi Rekabdarkolaee, Hossein & Wang, Qin, 2017. "Variable selection through adaptive MAVE," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 44-51.
    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. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    10. Chaouch, Mohamed, 2019. "Volatility estimation in a nonlinear heteroscedastic functional regression model with martingale difference errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 129-148.
    11. 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.

    More about this item

    Keywords

    Adaptive Estimation; Asymptotic Expansions; Efficiency; Kernel; Local Likelihood Estimation; Nonparametrie Regression;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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