2009/04/03 by Markus Reiß, Reiss, Markus, Yves Rozenholc +3
Decision Sciences · Engineering · Mathematics · #62F05 #62G08 #62G20 #62G35 #62P10 #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Fault Detection and Control Systems #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.0904.0543
openalex publication_date 2009/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.