We 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, ∞). 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.
Publié le : 2009-04-15
Classification:
Asymptotic distribution,
deconvolution,
decreasing density,
least squares,
maximum likelihood,
minimax risk,
62E20,
62G05
@article{1236693150,
author = {Jongbloed, Geurt and van der Meulen, Frank H.},
title = {Estimating a concave distribution function from data corrupted with additive noise},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 782-815},
language = {en},
url = {http://dml.mathdoc.fr/item/1236693150}
}
Jongbloed, Geurt; van der Meulen, Frank H. Estimating a concave distribution function from data corrupted with additive noise. Ann. Statist., Tome 37 (2009) no. 1, pp. 782-815. http://gdmltest.u-ga.fr/item/1236693150/