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Smoothing

Statistical and Numerical Computing

  1. Karen Kafadar1,
  2. Paul S. Horn2

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vas029

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Kafadar, K. and Horn, P. S. 2006. Smoothing. Encyclopedia of Environmetrics. 4.

Author Information

  1. 1

    University of Colorado, CO, USA

  2. 2

    University of Cincinnati Ohio, OH, USA

Publication History

  1. Published Online: 15 SEP 2006

This is not the most recent version of the article. View current version (15 JAN 2013)

Further Reading

  1. Further Reading
  2. References

Two particularly useful books on smoothing are Simonoff [21] and Bowman and Azzalini [1]; the former emphasizes applications of smoothing for density estimates, while the latter emphasizes more general smoothing applications as described in this entry. Both concentrate on one-dimensional smoothing. These books, as well as the entry on Nonparametric Regression Model, also discuss the issue of selecting a bandwidth. Ripley [20] and Cressie [5] offer more methods and examples for higher-dimensional data. O'Sullivan [18] presents a discussion of robust smoothing.

References

  1. Further Reading
  2. References
  • 1
    Bowman, A.W. & Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis, Oxford University Press, London.
  • 2
    Chen, L. (1997). Multivariate regression splines, Computational Statistics and Data Analysis 26, 7182.
  • 3
    Clayton, D. & Kaldor, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping, Biometrics 43, 671682.
  • 4
    Cleveland, W.S. & Devlin, S.J. (1988). Locally weighted regression: an approach to regression analysis by local fitting, Journal of the American Statistical Association 83, 596610.
  • 5
    Cressie, N. (1986). Kriging nonstationary data, Journal of the American Statistical Association 81, 625634.
  • 6
    Cressie, N. (1993). Statistics for Spatial Data, Revised Edition, Wiley, New York.
  • 7
    De Veaux, R.D., Bain, R. & Ungar, L.H. (1999). Hybrid neural network models for environmental process control, Environmetrics 10, 225236.
  • 8
    De Veaux, R.D., Gordon, A.L., Comiso, J.C. & Bacherer, N.E. (1993). Modeling of topographic effects on Antarctic sea ice using multivariate adaptive regression splines, Journal of Geophysical Research 98, 20 30720 319.
  • 9
    Donoho, D.L. & Johnstone, I.M. (1995). Adapting to unknown smoothness via wavelet shrinkage, Journal of the American Statistical Association 90, 12001224.
  • 10
    Friedman, J.H. (1991). Multivariate adaptive regression splines, The Annals of Statistics 19, 1141.
  • 11
    Goodall, C.R. (1991). A survey of smoothing techniques, in Modern Methods of Data Analysis, Chapter 3, J. Fox & J.S. Long, eds, Sage, Beverly Hills, pp. 126176.
  • 12
    Hall, P. (1998). Binning, in Encyclopedia of Statistical Sciences, Update Vol. 2, S. Kotz, C.B. Read & D.C. Banks, eds, Wiley, New York, pp. 6465.
  • 13
    Hastie, T. & Loader, C. (1993). Local regression: automatic kernel carpentry (with discussion), Statistical Science 8, 120143.
  • 14
    Mallows, C.L. (1980). Some theory of nonlinear smoothers, The Annals of Statistics 8, 695715.
  • 15
    Mathéron, G. (1963). Principles of geostatistics, Economic Geology 58, 12461266.
  • 16
    Mathsoft (1993). S-Plus, Unix Version.
  • 17
    Narendra, P.M. (1981). A separable median filter for image noise smoothing, IEEE Transactions on Pattern Analysis and Machine Intelligence 3, 2029.
  • 18
    O'Sullivan, F. (1988). Robust smoothing, in Encyclopedia of Statistical Sciences, Vol. 8, S. Kotz, N.L. Johnson & C. Read, eds, Wiley, New York, pp. 170173.
  • 19
    Ramsey, J.O. (1988). Monotone regression splines in action (with discussion), Statistical Science 3, 424461.
  • 20
    Ripley, B. (1981). Spatial Statistics, Wiley, New York.
  • 21
    Simonoff, J.S. (1996). Smoothing Methods in Statistics, Springer-Verlag, New York.
  • 22
    Tukey, J.W. (1977). Exploratory Data Analysis, Addison-Wesley, Reading.
  • 23
    Tukey, P.A. & Tukey, J.W. (1981). Graphic display of data sets in 3 or more dimensions, in Interpreting Multivariate Data, V. Barnett, ed., Wiley, Chichester, 1981, pp. 189275. [Reprinted in Cleveland, W.S., ed. (1988), The Collected Works of John W. Tukey, Vol. V: Graphics, 1965–1975, Wadsworth, Belmont, pp. 188288.]
  • 24
    Velleman, P.F. (1980). Definition and comparison of robust nonlinear data smoothing algorithms, Journal of the American Statistical Association 75, 609615.
  • 25
    Wahba, G. (1990). Spline Models for Observational Data, SIAM, Philadelphia.
  • 26
    Yang, C.J. & Huang, T.S. (1981). The effect of median filtering on edge location estimation, Computer Graphics and Image Processing 15, 224245.