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Kernel estimation of a partially linear additive model

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  • Manzan, Sebastiano
  • Zerom, Dawit

Abstract

In this paper, we introduce a kernel estimator for the finite-dimensional parameter of a partially linear additive model. Under some regularity conditions, we establish n1/2-consistency and asymptotic normality of the estimator. Unlike existing kernel-based estimators: Fan et al. (1998. Ann. Statist. 26, 943-971) and Fan and Li (2003. Statist. Sinica 13, 739-762) our estimator attains the semiparametric efficiency bound of the partially linear additive model under homoscedastic errors. We also show that when the true specification is the partially linear additive model, the proposed estimator is asymptotically more efficient than an estimator that ignores the additive structure.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 72 (2005)
Issue (Month): 4 (May)
Pages: 313-322

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Handle: RePEc:eee:stapro:v:72:y:2005:i:4:p:313-322

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Related research

Keywords: Additivity Kernel Partially linear additive model Semiparametric efficient;

References

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  1. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  2. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-96, May.
  3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  4. Li, Qi, 1996. "On the root-N-consistent semiparametric estimation of partially linear models," Economics Letters, Elsevier, vol. 51(3), pages 277-285, June.
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Citations

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Cited by:
  1. Cheng, Yebin & De Gooijer, Jan & Zerom, Dawit, 2009. "Efficient Estimation of an Additive Quantile Regression Model," MPRA Paper 14388, University Library of Munich, Germany.
  2. Yebin Cheng & Jan G. De Gooijer & Dawit Zerom, 2009. "Efficient Estimation of an Additive Quantile Regression," Tinbergen Institute Discussion Papers 09-104/4, Tinbergen Institute.
  3. Manzan, sebastiano & Zerom, Dawit, 2008. "A Semiparametric Analysis of Gasoline Demand in the US: Reexamining The Impact of Price," MPRA Paper 14386, University Library of Munich, Germany.
  4. Chuanhua Wei & Yubo Luo & Xizhi Wu, 2012. "Empirical likelihood for partially linear additive errors-in-variables models," Statistical Papers, Springer, vol. 53(2), pages 485-496, May.
  5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  6. Chuanhua Wei & Qihua Wang, 2012. "Statistical inference on restricted partially linear additive errors-in-variables models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(4), pages 757-774, December.

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