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An effective bandwidth selector in a complicated kernel regression

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Abstract

The field of nonparametrics has shown its appeal in recent years with an array of new tools for statistical analysis. As one of those tools, nonparametric regression has become a prominent statistical research topic and also has been well established as a useful tool. In this article we investigate the biased cross-validation selector, BCV, which is proposed by Ohet al. (1995), for a less smoothing regression function. In the simulation study, BCV selector is shown to perform well in practice with respect to ASE ratio.

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References

  1. C.-K. Chu and J. S. Marron,Choosing a Kernel Regression Estimator, Statistical Science6 (1991), 404–436.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. M. Clark,A Calibration Curve for Radio Carbon Dates, Antiquity49 (1975), 251–266.

    Google Scholar 

  3. P. Craven and G. Wahba,Smoothing Noisy Data With Spline Functions, Numerische Mathematik31 (1979), 377–403.

    Article  MATH  MathSciNet  Google Scholar 

  4. W. Härdle and R. J. Carroll,Biased Crossvalidation for a Kernel Regression Estimator and its Derivatives, Osterreichische Zeitschrift für Statistik und Informatik (ZSI)20 (1990), 53–64.

    Google Scholar 

  5. W. Härdle and J. S. Marron,Asymptotic Nonequivalence of Some Bandwidth Selectors in Nonparametric Regression, Biometrika72 (1985a), 481–484.

    MATH  MathSciNet  Google Scholar 

  6. W. Härdle and J. S. Marron,Optimal Bandwidth Selection in Nonparametric Regression Function Estimation, The Annals of Statistics13 (1985b), 1465–1481.

    Article  MATH  MathSciNet  Google Scholar 

  7. W. Härdle, P. Hall and J. S. Marron,How Far Are Automatically Chosen Regression Smoothing Parameters From Their Optimum?, Journal of the American Statistical Association83 (1988), 86–101.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. A. McDonald and A. Owen,Smoothing With Splem Linear Fits, Technometrics28 (1986), 195–208.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. C. Oh, B. C. Kim, J. S. Lee and B. U. Park,Biased Cross-Validation in a Kernel Regression Estimation, J. Jpn. Soc. Comp. Statist.8 (1995), 57–68.

    MathSciNet  Google Scholar 

  10. J. Rice,Bandwidth Choice for Nonparametric Regression, The Annals of Statistics12 (1984), 1215–1230.

    Article  MATH  MathSciNet  Google Scholar 

  11. D. Ruppert, S. J. Sheather and M. P. Wand,An Effective Bandwidth Selector for Local Least Squares Regression, Journal of the American Statistical Association90 (1995), 1257–1270.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. W. Scott and G. R. Terrell,Biased and Unbiased Cross-Validation in Density Estimation, Journal of the American Statistical Association82 (1987), 1131–1146.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Shibata,An Optimal Selection of Regression Variables, Biometrika68 (1981), 45–54.

    Article  MATH  MathSciNet  Google Scholar 

  14. G. Wahba and S. Wold,A Completely Automatic French Curve: Fitting Spline Functions by Cross-validation, Comm. Statist.4 (1975), 1–17.

    Article  MathSciNet  Google Scholar 

  15. W. H. Press, B. P. Flannery, S. A. Teukolsky and W.T. Vetterling,Numerical Recipes: the Art of Scientific Computing, Cambridge University Press, Cambridge, 1986.

    Google Scholar 

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Oh, J.C. An effective bandwidth selector in a complicated kernel regression. Korean J. Com. & Appl. Math. 3, 205–215 (1996). https://doi.org/10.1007/BF03008902

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