$L_2$ boosting in kernel regression

Details $L_2$ boosting in kernel regression $L_2$ boosting in kernel regression

2009-09-04

arxiv.org/abs/0909.0833v1

Bernoulli 2009, Vol. 15, No. 3, 599-613

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ160

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.

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