Pointwise adaptive estimation for quantile regression - Markus Reiß; Yves Rozenholc; Charles A. Cuenod (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2011)
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.
Keywords: C14; C31; 330; M-estimation; median regression; robust estimation; local model selection; unsupervised learning; local bandwidth selection; median filter; Lepski procedure; minimax rate; image denoising; Regression; Nichtparametrisches Verfahren; Schätztheorie; Theorie