A Kiefer–Wolfowitz comparison theorem for Wicksell’s problem

研究问题: 在由天文学暗物质分布估计所推动的 Wicksell 问题中，经验分布与其最小凹上包络之间的差异能以多快速度收敛？
方法与思路: 作者将 Wicksell 问题的保序分析扩展至回归函数估计，建立比较经验分布与最小凹上包络的 Kiefer–Wolfowitz 型定理。
材料陈述的贡献: 摘要称，比较定理给出 n^{-1}log n 的速率，快于所列 n^{-2/3}log n 速率，并可用于获得保序及平滑估计的渐近分布。
阅读关注点: 应核对比较对象、误差度量及速率成立的条件，并查看该定理如何用于保序和平滑估计量，区分逼近速率与估计收敛率。
阅读边界: 仅据版本未注明的 OpenAlex 索引摘要；范数、概率意义和正则条件未说明，不能把比较速率直接当作所有估计量的收敛率。

GPT-6.1 Sol · 高 · 2026-10-05

原文摘要

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.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.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）

笔记与分组

分类依据与纠错

A Kiefer–Wolfowitz comparison theorem for Wicksell’s problem

代码、数据与补充材料

Wicksell 问题的 Kiefer–Wolfowitz 比较定理

原文摘要

同方向的基础文献

同方向的基础文献