Isotonic estimation and rates of convergence in Wicksell's problem
Isotonic estimation and rates of convergence in Wicksell's problem
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DOI：
10.1214/aos/1176324310
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发表时间：
1995-10-01
影响因子：
4.5
通讯作者：
Jongbloed, G
中科院分区：
文献类型：
--
作者：
Groeneboom, P;Jongbloed, G
它表明，在非参数设置为所谓的Wicksell问题，球的平方半径的分布函数不能估计的速度快于n（-1/2）根log n。我们提出了一个保序估计的分布函数，达到这个速度，并推导出其渐近（正态）分布。它表明，这种限制分布的方差是完全一半的渐近方差的天真插件估计。
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)root 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.