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Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion

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  • Martins-Filho, Carlos
  • yang, ke

Abstract

In this paper, we investigate the finite sample performance of four kernel-based estimators that are currently available for additive non-parametric regression models—the classic backfitting estimator (CBE), the smooth backfitting estimator, the marginal integration estimator, and two versions of a two-stage estimator of which the first is proposed by Kim, Linton and Hengartner (1999) and the second is proposed in this paper. The bandwidths are selected for each estimator by minimizing their respective asymptotic approximation of the mean average squared errors. In our simulations, we are particularly concerned with the performance of these estimators under this unified data-driven bandwidth selection method, since in this case both the asymptotic and the finite sample properties of all estimators are currently unavailable. The comparison is based on the estimators' average squared error. Our Monte Carlo results seem to suggest that the CBE is the best performing kernel-based procedure.

Suggested Citation

  • Martins-Filho, Carlos & yang, ke, 2007. "Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion," MPRA Paper 39295, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:39295
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    References listed on IDEAS

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    1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    2. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    3. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    4. Opsomer, Jean D. & Ruppert, D., 1998. "A Fully Automated Bandwidth Selection Method for Fitting Additive Models," Staff General Research Papers Archive 1176, Iowa State University, Department of Economics.
    5. Stefan Sperlich & Oliver Linton & Wolfgang Härdle, 1999. "Integration and backfitting methods in additive models-finite sample properties and comparison," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 419-458, December.
    6. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61, February.
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    Citations

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    Cited by:

    1. Wang, Li & Wang, Suojin, 2011. "Nonparametric additive model-assisted estimation for survey data," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1126-1140, August.
    2. Song, Qiongxia & Yang, Lijian, 2010. "Oracally efficient spline smoothing of nonlinear additive autoregression models with simultaneous confidence band," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2008-2025, October.
    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. Deniz Ozabaci & Daniel Henderson, 2015. "Additive kernel estimates of returns to schooling," Empirical Economics, Springer, vol. 48(1), pages 227-251, February.
    5. Guo, Zheng-Feng & Shintani, Mototsugu, 2011. "Nonparametric lag selection for nonlinear additive autoregressive models," Economics Letters, Elsevier, vol. 111(2), pages 131-134, May.
    6. Martins-Filho, Carlos & Yao, Feng, 2012. "Kernel-based estimation of semiparametric regression in triangular systems," Economics Letters, Elsevier, vol. 115(1), pages 24-27.
    7. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.

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    More about this item

    Keywords

    Additive non-parametric regression; Local linear estimation; Backfitting estimation; Smooth backfitting; Marginal integration;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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