What Criterion for a Power Algorithm?

  • Andreas Buja
Part of the Lecture Notes in Statistics book series (LNS, volume 109)


If Breiman and Friedman’s ACE algorithm is used with smoothing splines as building blocks, the question arises what criterion is being optimized. The obvious guess turns out to be wrong. The problem is that the building blocks are no longer orthogonal projections in the usual inner product. We describe the non-standard inner product that does yield orthogonal projections, and we indicate what the resulting “penalized R 2”-criterion is.

Key words and phrases

ACE power algorithms curve fitting smoothing splines penalty-based regularization response transformation 

AMS 1991 subject classifications

Primary 62G07 secondary 62H25 


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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Andreas Buja
    • 1
  1. 1.AT&T Bell LaboratoriesNew JerseyUSA

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