Estimating a concave distribution function from data corrupted with additive noise
| dc.creator | Jongbloed, Geurt | |
| dc.creator | van der Meulen, Frank H. | |
| dc.date | 2009-04-01 | |
| dc.date.accessioned | 2026-07-07T12:59:00Z | |
| dc.date.available | 2026-07-07T12:59:00Z | |
| dc.description | 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 $(0,\infty)$. 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. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/0904.0091 | |
| dc.identifier | http://arxiv.org/abs/0904.0091 | |
| dc.identifier | Annals of Statistics 2009, Vol. 37, No. 2, 782-815 | |
| dc.identifier | doi:10.1214/07-AOS579 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225438 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62E20, 62G05 (Primary) | |
| dc.title | Estimating a concave distribution function from data corrupted with additive noise | |
| dc.type | text |