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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)

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Figure 1. Four sets of smoothing a sequence of 20 data points. (a) Running means of length 3 on a sequence with an abrupt ridge. (b) Running medians of length 3 on a sequence with an abrupt ridge. (c) Running means of length 3 on a sequence with an outlier. (d) Running medians of length 3 on a sequence with an outlier

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Figure 2. Monthly carbon dioxide concentrations in Mauna Loa volcano, from January 1959 to December 1990. Data from S-PLUS statistical software [16]

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Figure 3. Residuals from fitting a quadratic trend and month effect to the data in Figure 2

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Figure 4. Five smoothers of the residuals shown in Figure 3. In order of smoothness: running medians of length 3 (least smooth), running medians of length 5, running medians of length 11, loess with span 0.10, loess with span 0.25 (most smooth)

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Figure 5. Nonlinear smoothers to two-dimensional data. (a) Smooth surface with no error. (b) Smooth surface with additive N(0, 0.01) error. (c) Median polish fit to the data in panel (b). (d) Cressie's median polish smoother to the data in panel (b). (e) Loess smoother (span 0.10) on the data in panel (b). (f) Loess smoother (span 0.30) on the data in panel (b)