Empirical Likelihood for Random Sets
Empirical Likelihood for Random Sets
复制标题
随机集的经验似然
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Taisuke Otsu
中科院分区：
文献类型：
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作者：
Karun Adusumilli;Taisuke Otsu
摘要在许多统计应用中，观测数据采用集合的形式而不是点的形式。例如，测量分析中的括号数据，形态分析中的肿瘤生长和岩石颗粒图像，以及医学成像和机器人视觉中凸集支撑函数的噪声测量。此外，在治疗效应的研究中，研究人员经常希望对可用随机集表示的效应的非参数界进行推断。本文发展了随机集的非参数似然及其均值的概念，即欧曼期望，并应用经验似然理论提出了一般的推断方法。几个例子，如与括号收入数据的回归，肿瘤生长的布尔模型，治疗效果的界限分析，以及通过支持函数进行图像分析，说明了所提出的方法的有效性。这篇文章的补充材料可以在网上找到。
Abstract In many statistical applications, the observed data take the form of sets rather than points. Examples include bracket data in survey analysis, tumor growth and rock grain images in morphology analysis, and noisy measurements on the support function of a convex set in medical imaging and robotic vision. Additionally, in studies of treatment effects, researchers often wish to conduct inference on nonparametric bounds for the effects which can be expressed by means of random sets. This article develops the concept of nonparametric likelihood for random sets and its mean, known as the Aumann expectation, and proposes general inference methods by adapting the theory of empirical likelihood. Several examples, such as regression with bracket income data, Boolean models for tumor growth, bound analysis on treatment effects, and image analysis via support functions, illustrate the usefulness of the proposed methods. Supplementary materials for this article are available online.