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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.

Suggested Citation

  • Manzan, Sebastiano & Zerom, Dawit, 2005. "Kernel estimation of a partially linear additive model," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 313-322, May.
  • Handle: RePEc:eee:stapro:v:72:y:2005:i:4:p:313-322
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    References listed on IDEAS

    as
    1. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Li, Qi, 1996. "On the root-N-consistent semiparametric estimation of partially linear models," Economics Letters, Elsevier, vol. 51(3), pages 277-285, June.
    4. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
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    Citations

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    Cited by:

    1. Yebin Cheng & Jan G. De Gooijer & Dawit Zerom, 2011. "Efficient Estimation of an Additive Quantile Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 46-62, March.
    2. 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.
    3. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.
    4. 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;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 757-774, December.
    5. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    7. Deniz Ozabaci & Daniel Henderson, 2015. "Additive kernel estimates of returns to schooling," Empirical Economics, Springer, vol. 48(1), pages 227-251, February.
    8. 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.

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