Translator Disclaimer
August 2007 A Kiefer–Wolfowitz comparison theorem for Wicksell’s problem
Xiao Wang, Michael Woodroofe
Ann. Statist. 35(4): 1559-1575 (August 2007). DOI: 10.1214/009053606000001604

Abstract

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.

Citation

Download Citation

Xiao Wang. Michael Woodroofe. "A Kiefer–Wolfowitz comparison theorem for Wicksell’s problem." Ann. Statist. 35 (4) 1559 - 1575, August 2007. https://doi.org/10.1214/009053606000001604

Information

Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1209.62082
MathSciNet: MR2351097
Digital Object Identifier: 10.1214/009053606000001604

Subjects:
Primary: 62G05, 62G08, 62G20

Rights: Copyright © 2007 Institute of Mathematical Statistics

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.35 • No. 4 • August 2007
Back to Top