J Austral Math Soc Ser A 57 pp316--329, 1994.

Convergence of the Backfitting Algorithm for Additive Models

Craig F. Ansley and Robert Kohn

Abstract

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 altenating projection theorem.

1991 AMS Subject Classification: 62G05, 62J05, 65D07, 65D10

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Authors

Craig F. Ansley

Department of Accounting and Finance, University of Auckland, Private Bag, Auckland, New Zealand.

Robert Kohn

Australian Graduate School of Management, University of NSW, Kensington, New South Wales, Australia.