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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.

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File URL: http://sticerd.lse.ac.uk/dps/em/em419.pdf
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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2001/419.

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Date of creation: Jun 2001
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Handle: RePEc:cep:stiecm:/2001/419

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

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

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  1. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
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Cited by:
  1. 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.
  2. Wang, Dong, 2010. "Modeling epigenetic modifications under multiple treatment conditions," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1179-1189, April.
  3. Yao, Weixin, 2013. "A note on EM algorithm for mixture models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 519-526.
  4. 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.
  5. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.

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