Recursive Bias Estimation and L_2 Boosting

01/30/2008

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by   Pierre Andre Cornillon, et al.

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This paper presents a general iterative bias correction procedure for regression smoothers. This bias reduction schema is shown to correspond operationally to the L_2 Boosting algorithm and provides a new statistical interpretation for L_2 Boosting. We analyze the behavior of the Boosting algorithm applied to common smoothers S which we show depend on the spectrum of I-S. We present examples of common smoother for which Boosting generates a divergent sequence. The statistical interpretation suggest combining algorithm with an appropriate stopping rule for the iterative procedure. Finally we illustrate the practical finite sample performances of the iterative smoother via a simulation study. simulations.