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Surface Fitting With Orthogonal Additive Models

In: Computing Science and Statistics

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  • Paul Speckman

    (University of Missouri-Columbia, Department of Statistics)

Abstract

A number of algorithms such as projection pursuit and backfitting have been proposed for using one-dimensional smoothers to fit additive models in several dimensions. This talk treats a simple variant, additive approximations to a response surface based on orthogonalized regressors. The idea is motivated by OLS where useful diagnostics can be based on partial residuals, and many of the ideas from OLS carry over to the situation where projection is replaced by smoothing. In particular, one can use forward selection. At each stage, a one-dimension al smoother is used to add the effect of the regressor not in the current model which best fits the residuals, and data smoothing is used to transform the remaining regressors to be approximately orthogonal to those in the model. Because of this approximate orthogonalization, a one-pass algorithm can be effective in obtaining estimates, and iteration via backfitting is unnecessary.

Suggested Citation

  • Paul Speckman, 1992. "Surface Fitting With Orthogonal Additive Models," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 534-538, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_94
    DOI: 10.1007/978-1-4612-2856-1_94
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