Pointwise adaptive estimation for robust and quantile regression

Details Pointwise adaptive estimation for robust and quantile regression Pointwise adaptive estimation for robust and quantile regression

2009-04-03

arxiv.org/abs/0904.0543v1

Mathematics

Statistics Theory

Scientific paper

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is extended to image denoising and applied to CT scans in cancer research.

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