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  • Convergence of the backfitting algorithm for additive models

  • Part of
  • Craig F. Ansley, Robert Kohn
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 57 / Issue 3 / December 1994
    Published online by Cambridge University Press:
    09 April 2009, pp. 316-329
    Print publication:
    December 1994
    • Article
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  • The backfitting algorithm is an iterative procedure for fitting additive models in which, at each step, one component is estimated keeping the other components fixed, the algorithm proceeding component by component and iterating until convergence. Convergence of the algorithm has been studied by Buja, Hastie, and Tibshirani (1989). We give a simple, but more general, geometric proof of the convergence of the backfitting algorithm when the additive components are estimated by penalized least squares. Our treatment covers spline smoothers and structural time series models, and we give a full discussion of the degenerate case. Our proof is based on Halperin's (1962) generalization of von Neumann's alternating projection theorem.