Open Access
October, 1995 Isotonic Estimation and Rates of Convergence in Wicksell's Problem
Piet Groeneboom, Geurt Jongbloed
Ann. Statist. 23(5): 1518-1542 (October, 1995). DOI: 10.1214/aos/1176324310


It is shown that, in the nonparametric setting for the so-called Wicksell problem, the distribution function of the squared radii of the balls cannot be estimated at a rate faster than $n^{-1/2}\sqrt{\log n}$. We present an isotonic estimator of the distribution function which attains this rate and derive its asymptotic (normal) distribution. It is shown that the variance of this limiting distribution is exactly half the asymptotic variance of the naive plug-in estimator.


Download Citation

Piet Groeneboom. Geurt Jongbloed. "Isotonic Estimation and Rates of Convergence in Wicksell's Problem." Ann. Statist. 23 (5) 1518 - 1542, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62034
MathSciNet: MR1370294
Digital Object Identifier: 10.1214/aos/1176324310

Primary: 62G05
Secondary: 62E20

Keywords: $\arg \max$ functionals , asymptotic distribution , Inverse problems , Minimax rate

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 5 • October, 1995
Back to Top