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Non-parametric regression and density estimation under control of modality

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COMPSTAT
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Abstract

Most available methods in non-parametric regression and density estimation are not directly concerned with modality. New methods are presented that avoid artifacts and yield estimates that have asymptotically the correct modality.

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References

  • Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. and Picard, D. (1995). Wavelet shrinkage: asymptopia?. Journal of the Royal Statistical Society, Ser. B, 57, 371–394.

    MathSciNet  Google Scholar 

  • Davies, P.L. (1995). Data features. Statistica Neerlandica, 49, 185–245.

    Article  MathSciNet  MATH  Google Scholar 

  • Davies, P.L. (1999). Hidden periodicities and strings. Technical Report, University of Essen.

    Google Scholar 

  • Davies, P.L. and Kovac, A. (1999). Modality, Runs, Strings and Multiresolution. Technical Report 16/99, Sonderforschungsbereich 475, University of Dortmund.

    Google Scholar 

  • Dümbgen, L. (1998). New goodness-of-fit tests and their application to non-parametric confidence sets. The Annals of Statistics, 26, 288–314.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and its Applica-tions. London: Chapman and Hall.

    Google Scholar 

  • Härdle, W., Kerkyacharian, G., Picard, D. and Tsybakov, A. (1998). Wavelets, Approximation, and Statistical Applications. New York: Springer-Verlag.

    Google Scholar 

  • Hartigan, J.A. and Hartigan, P.M. (1985). The dip test of unimodality. The Annals of Statistics, 13, 70–84.

    Article  MathSciNet  MATH  Google Scholar 

  • Kovac, A. and Silverman, B. W. (2000). Extending the Scope of Wavelet Regression Methods by Coefficient-dependent Thresholding Journal of the American Statistical Association, to appear.

    Google Scholar 

  • Mammen, E. and van de Geer, S. (1997). Locally adaptive regression splines. The Annals of Statistics, 25, 387–413.

    Article  MathSciNet  MATH  Google Scholar 

  • Marron, J.S. and Tsybakov, A.B. (1995). Visual error criteria for qualitative smoothing. Journal of the American Statistical Association, 90, 499–507.

    Article  MathSciNet  MATH  Google Scholar 

  • Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and its Applications, 10, 186–190.

    Article  Google Scholar 

  • Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Ser. B,53, 683–690.

    MathSciNet  MATH  Google Scholar 

  • Silverman, B. W. (1985). Some aspects of the spline smoothing approach to non-parametric regre ssion curve fitting. Journal of the Royal Statistical Society,Ser. B, 47, 1–52.

    MATH  Google Scholar 

  • Watson, G. S. (1964). Smooth regression analysis. Sankhyā, Ser. A, 26, 101–116.

    MATH  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Davies, P.L., Kovac, A. (2000). Non-parametric regression and density estimation under control of modality. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57678-2_30

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  • DOI: https://doi.org/10.1007/978-3-642-57678-2_30

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1326-5

  • Online ISBN: 978-3-642-57678-2

  • eBook Packages: Springer Book Archive

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