2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130818We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the excess risk, that is, rates that can be faster than n^{-1/2}, where n is the sample size. We show that our method also gives adaptive estimators for the problem of edge estimation.Published at http://dx.doi.org/10.1214/009053604000001066 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62G07, 62G08, 62H30, 68T10 (Primary)text