2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225438We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational algorithm. For the LS estimator and its derivative, we also derive the pointwise asymptotic distribution. Moreover, the rate $n^{-2/5}$ achieved by the LS estimator is shown to be minimax for estimating the distribution function at a fixed point.Published in at http://dx.doi.org/10.1214/07-AOS579 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62E20, 62G05 (Primary)text