A Kiefer--Wolfowitz comparison theorem for Wicksell's problem
| dc.creator | Wang, Xiao | |
| dc.creator | Woodroofe, Michael | |
| dc.date | 2006-11-03 | |
| dc.date | 2007-10-18 | |
| dc.date.accessioned | 2026-07-07T08:40:51Z | |
| dc.date.available | 2026-07-07T08:40:51Z | |
| dc.description | We extend the isotonic analysis for Wicksell's problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a version of the Kiefer--Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate $n^{-1}\log n$ faster than $n^{-2/3}\log n$. The main result is useful in obtaining asymptotic distributions for estimators, such as isotonic and smooth estimators. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009053606000001604 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/math/0611088 | |
| dc.identifier | http://arxiv.org/abs/math/0611088 | |
| dc.identifier | Annals of Statistics 2007, Vol. 35, No. 4, 1559-1575 | |
| dc.identifier | doi:10.1214/009053606000001604 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141495 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G05, 62G08, 62G20 (Primary) | |
| dc.title | A Kiefer--Wolfowitz comparison theorem for Wicksell's problem | |
| dc.type | text |