Open Access
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


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.


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


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

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

Primary: 62G05 , 62G08 , 62G20

Keywords: dark matter , Empirical processes , isotonic estimation , least concave majorant , regression function , velocity dispersions

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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