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A Personal View of Smoothing and Statistics

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Statistical Theory and Computational Aspects of Smoothing

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Summary

Personal views are offered on the foundations of smoothing methods in statistics. Key points are that smoothing is a useful tool in data analysis, and that the field of data based smoothing parameter selection has matured to the point that effective methods are ready for use as defaults in software packages. A broader lesson available from the discussion is: a combination of computational methods and mathematical statistics is a powerful research tool.

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References

  1. Cao, R., Cuevas, A. and González-Manteiga, W. (1994). A comparative study of several smoothing methods in density estimation. Comp. Statist. Data Anal 17 153–176.

    Article  Google Scholar 

  2. Cleveland, W. S. (1985) The elements of graphing data, Wadsworth, Belmont, California.

    Google Scholar 

  3. Cleveland, W. S. (1993) Visualizing data, Hobart Press, Summit, New Jersey.

    Google Scholar 

  4. Eubank, R. L. (1988) Spline Smoothing and Nonparametric Regression, Dekker, New York.

    Google Scholar 

  5. Green, P. and Silverman, B. W. (1994) Nonparametric Regression and generalized linear models, a roughness penalty approach, Chapman and Hall, London.

    Google Scholar 

  6. Härdle, W. (1991) Applied Nonparametric Regression, Cambridge University Press, Boston.

    Google Scholar 

  7. Hall, P. (1980) Objective methods for the estimation of window size in the nonparametric estimation of a density. Unpublished manuscript.

    Google Scholar 

  8. Hall, P. and Marron, J. S. (1991b) Lower bounds for bandwidth selection in density estimation. Probab. Theory Related Fields 90, 149–173.

    Article  Google Scholar 

  9. Hastie, T. J. and Tibshirani, R. J. (1990) Generalized additive models, Chapman and Hall, London.

    Google Scholar 

  10. Jones, M. C., Marron, J. S. and Sheather, S. J. (1992) Progress in data based bandwidth selection for kernel density estimation, submitted to J. Nonpar. Statist.

    Google Scholar 

  11. Jones, M. C., Marron, J. S. and Sheather, S. J. (1994) A brief survey of modern bandwidth selection methods, submitted to J. Amer. Statist. Assoc.

    Google Scholar 

  12. Marron, J.S., and Tsybakov, A.B. (1995), “Visual Error Criteria for Qualitative Smoothing,” Journal of the American Statistical Association, 90, 499–507.

    Article  Google Scholar 

  13. Marron, J. S. and Wand, M. P. (1992). Exact mean integrated squared error,Ann. Statist. 20, 712–736.

    Article  Google Scholar 

  14. Müller, H.-G. (1988) Nonparametric regression analysis of longitudinal data. Springer Verlag, Berlin.

    Book  Google Scholar 

  15. Park, B.-U. and Marron, J. S. (1990). Comparison of data-driven bandwidth selectors. J. Amer. Statist. Assoc. 85 66–72.

    Article  Google Scholar 

  16. Park, B.-U. and Turlach, B. A. (1992) Practical performance of several data driven bandwidth selectors (with discussion). Comput. Statist. 7 251–285.

    Google Scholar 

  17. Scott, D. W. and Factor, L. E. (1981) Monte Carlo study of three data- based nonparametric probability density estimators. J. Amer. Statist. Assoc. 76 9–15.

    Article  Google Scholar 

  18. Scott, D. W. and Terrell, G. R. (1987) Biased and unbiased cross-validation in density estimation. J. Amer. Statist. Assoc. 82 1131–1146.

    Article  Google Scholar 

  19. Scott, D. W. (1992) Multivariate density estimation: theory, practice and visualization. Wiley, New York.

    Google Scholar 

  20. Sheather, S. J. (1986). A data-based algorithm for choosing the window width when estimating the density at a point. Comput. Statist. Data Anal. 1 229–238.

    Article  Google Scholar 

  21. Sheather, S. J. (1986). An improved data-based algorithm for choosing the window width when estimating the density at a point. Comput. Statist. Data Anal. 4 61–65.

    Article  Google Scholar 

  22. Sheather, S. J. (1992). The performance of six popular bandwidth selection methods on some real data sets (with discussion). Comput. Statist. 7, 225–250.

    Google Scholar 

  23. Silverman, B.W. (1986) Density estimation for statistics and data analysis, Chapman and Hall, New York.

    Google Scholar 

  24. Wahba, G. (1990) Spline Models for Observational Data, SIAM, Philadelphia.

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics, University of North Carolina, Chapel Hill, 27599-3260, NC, USA

    J. S. Marron

Authors
  1. J. S. Marron
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Editor information

Editors and Affiliations

  1. Center for Computational Statistics Institut für Statistik und Ökonometrie Wirtschaftswissenschaftliche Fakultät, Humboldt-Universität zu Berlin, Spandauer straße 1, D-10178, Berlin, Germany

    Wolfgang Härdle

  2. Medical Biometrics Group, University of Graz Medical Schools, Auenbruggerplatz 30/IV, A-8036, Graz, Austria

    Michael G. Schimek

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© 1996 Physica-Verlag Heidelberg

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Marron, J.S. (1996). A Personal View of Smoothing and Statistics. In: Härdle, W., Schimek, M.G. (eds) Statistical Theory and Computational Aspects of Smoothing. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48425-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-48425-4_1

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-7908-0930-5

  • Online ISBN: 978-3-642-48425-4

  • eBook Packages: Springer Book Archive

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