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Title:Pointwise adaptive estimation for quantile regression PDF Logo
Authors:Reiß, Markus
Rozenholc, Yves
Cuenod, Charles A.
Issue Date:2011
Series/Report no.:SFB 649 discussion paper 2011-029
Abstract:A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, 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 the basis for denoising CT scans in cancer research.
median regression
robust estimation
local model selection
unsupervised learning
local bandwidth selection
median filter
Lepski procedure
minimax rate
image denoising
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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