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Plug-in method for nonparametric regression

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Abstract

The problem of bandwidth selection for non-parametric kernel regression is considered. We will follow the Nadaraya–Watson and local linear estimator especially. The circular design is assumed in this work to avoid the difficulties caused by boundary effects. Most of bandwidth selectors are based on the residual sum of squares (RSS). It is often observed in simulation studies that these selectors are biased toward undersmoothing. This leads to consideration of a procedure which stabilizes the RSS by modifying the periodogram of the observations. As a result of this procedure, we obtain an estimation of unknown parameters of average mean square error function (AMSE). This process is known as a plug-in method. Simulation studies suggest that the plug-in method could have preferable properties to the classical one.

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References

  • Cleveland WS (1979) Robust locally weighted regression and smoothing scatter plots. J Am Stat Assoc 74:829–836

    Article  MATH  MathSciNet  Google Scholar 

  • Craven P, Wahba G (1979) Smoothing noisy data with spline function. Numer Math 31:377–403

    Article  MATH  MathSciNet  Google Scholar 

  • Chiu ST (1991) Some stabilized bandwidth selectors for nonparametric regression. Ann Stat 19:1528–1546

    Article  MATH  MathSciNet  Google Scholar 

  • Chiu ST (1990) Why bandwidth selectors tend to choose smaller bandwidths, and a remedy. Biometrika 77:222–226

    Article  MATH  MathSciNet  Google Scholar 

  • Droge B (1996) Some comments on cross-validation. Stat Theory Comput Aspects Smooth 178–199

  • Härdle W (1990) Applied nonparametric regression. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Härdle W, Hall P, Marron JS (1988) How far are automatically chosen regression smoothing parameters from their optimum? J Am Stat Assoc 83:86–95

    Article  MATH  Google Scholar 

  • Koláček J (2005) Kernel estimation of the regression function. PhD-thesis, Brno

  • Nadaraya EA (1964) On estimating regression. Theory Probab Appl 10:186–190

    Article  Google Scholar 

  • Rice J (1984) Bandwidth choice for nonparametric regression. Ann Stat 12:1215–1230

    Article  MATH  MathSciNet  Google Scholar 

  • Silverman BW (1985) Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J Roy Stat Soc Ser B 47:1–52

    MATH  Google Scholar 

  • Stone CJ (1977) Consistent nonparametric regression. Ann Stat 5:595–645

    Article  MATH  Google Scholar 

  • Wand MP, Jones MC (1995) Kernel smoothing. Chapman & Hall, London

    MATH  Google Scholar 

  • Watson GS (1964) Smooth regression analysis. Shankya Ser A 26:359–372

    MATH  Google Scholar 

Download references

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Correspondence to Jan Koláček.

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Supported by the MSMT: LC 06024.

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Koláček, J. Plug-in method for nonparametric regression. Computational Statistics 23, 63–78 (2008). https://doi.org/10.1007/s00180-007-0068-6

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  • DOI: https://doi.org/10.1007/s00180-007-0068-6

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