Recursive Bias Estimation and $L_2$ Boosting

Abstract

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.