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On boosting kernel regression. (English) Zbl 1182.62091
Summary: We propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya-Watson estimator with $$L_{2}$$ boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast, and the variance diverges exponentially slow. The first boosting step is analysed in more detail, giving asymptotic expressions as functions of the smoothing parameter, and relationships with previous work are explored. Practical performance is illustrated by both simulated and real data.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62J02 General nonlinear regression 65C60 Computational problems in statistics (MSC2010) 62G05 Nonparametric estimation
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