What Criterion for a Power Algorithm?
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 phrasesACE power algorithms curve fitting smoothing splines penalty-based regularization response transformation
AMS 1991 subject classificationsPrimary 62G07 secondary 62H25
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