Recursive Bias Estimation and $L_2$ Boosting

Details Recursive Bias Estimation and $L_2$ Boosting Recursive Bias Estimation and $L_2$ Boosting

2008-01-30

arxiv.org/abs/0801.4629v1

Statistics

Methodology

Scientific paper

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.

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