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September, 1990 Remarks on Functional Canonical Variates, Alternating Least Squares Methods and Ace
Andreas Buja
Ann. Statist. 18(3): 1032-1069 (September, 1990). DOI: 10.1214/aos/1176347739


We discuss properties of some data-analytic methods which are intimately related to each other: alternating least squares (ALS), correspondence analysis and more recently Breiman and Friedman's ACE algorithm. The application of these methods to regression produces nonparametric estimators of nonlinear transformations, both of the response and the predictors. These procedures are among the most powerful tools for data analysis, but missing awareness of some artifacts could lead to inappropriate interpretations. We point out some anomalies as well as some curiosities in the mathematics of these methods, and we relate them to some areas in computer-aided tomography, projection pursuit regression and nonlinear devices in the theory of noise.


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Andreas Buja. "Remarks on Functional Canonical Variates, Alternating Least Squares Methods and Ace." Ann. Statist. 18 (3) 1032 - 1069, September, 1990.


Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0721.62068
MathSciNet: MR1062698
Digital Object Identifier: 10.1214/aos/1176347739

Primary: 62J99
Secondary: 62P15

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 3 • September, 1990
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