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Speaking Stata: Smoothing in various directions

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  • Nicholas J. Cox

    (Durham University, UK)

Abstract

Identifying patterns in bivariate data on a scatterplot remains a ba- sic statistical problem, with special flavor when both variables are on the same footing. Ideas of double, diagonal, and polar smoothing inspired by Cleveland and McGill’s 1984 paper in the Journal of the American Statistical Association are revisited with various examples from environmental datasets. Double smooth- ing means smoothing both y given x and x given y. Diagonal smoothing means smoothing based on the sum and difference of y and x that treats the two variables symmetrically, possibly under standardization. Polar smoothing is based on the transformation from Cartesian to polar coordinates followed by smoothing and then reverse transformation; here the smoothing is implemented by regression on a series of sine and cosine terms. These methods thus offer exploratory tools for determining the broad structure of bivariate data.

Suggested Citation

  • Nicholas J. Cox, 2005. "Speaking Stata: Smoothing in various directions," Stata Journal, StataCorp LP, vol. 5(4), pages 574-593, December.
    • Handle: RePEc:tsj:stataj:v:5:y:2005:i:4:p:574-593
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    References listed on IDEAS

    as
    1. Peter Sasieni & Patrick Royston, 1998. "Pointwise confidence intervals for running," Stata Technical Bulletin, StataCorp LP, vol. 7(41).
    2. William D. Dupont & W. Dale Plummer, Jr., 2005. "Using density-distribution sunflower plots to explore bivariate relationships in dense data," Stata Journal, StataCorp LP, vol. 5(3), pages 371-384, September.
    3. Peter Sasieni, 1995. "Symmetric nearest neighbor linear smoothers," Stata Technical Bulletin, StataCorp LP, vol. 4(24).
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    Cited by:

    1. Maiti, Dibyendu & Bhattacharyya, Chandril, 2020. "Informality, enforcement and growth," Economic Modelling, Elsevier, vol. 84(C), pages 259-274.

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