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A Nonparametric Regression Estimator that Adapts to Error Distribution of Unknown Form

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  • Oliver Linton
  • Zhijie Xiao

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

  • Oliver Linton & Zhijie Xiao, 2001. "A Nonparametric Regression Estimator that Adapts to Error Distribution of Unknown Form," STICERD - Econometrics Paper Series 419, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:419
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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. repec:eee:jmvana:v:170:y:2019:i:c:p:129-148 is not listed on IDEAS
    3. Linton, O. & Xiao, Z., 2019. "Efficient Estimation of Nonparametric Regression in The Presence of Dynamic Heteroskedasticity," Cambridge Working Papers in Economics 1907, Faculty of Economics, University of Cambridge.
    4. 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.
    5. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    6. repec:eee:stapro:v:128:y:2017:i:c:p:44-51 is not listed on IDEAS
    7. 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.
    8. Yao, Weixin, 2013. "A note on EM algorithm for mixture models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 519-526.
    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.

    More about this item

    Keywords

    Adaptive estimation; asymptotic expansions; efficiency; kernel; local likelihood estimation; nonparametric regression.;

    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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