2008/06/25 by Charles Mitchell, Mitchell, Charles, Sara van de Geer +1
Engineering · Mathematics · #62G05 (Primary) 62G20 (Secondary) #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G20 #stat.TH
paper · pdf · doi:10.48550/arxiv.0806.4140
Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2008/06/25 · openalex publication_date 2008/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the tails of the losses used. Starting with examples from the 3 basic estimation problems, regression, classification and density estimation, we formulate risk bounds for empirical risk minimization under successively weakening conditions and prove them at a very general level, for general margin and power tail behavior of the excess losses.