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Empirical likelihood for random sets

Adusumilli, Karun and Otsu, Taisuke (2017) Empirical likelihood for random sets. Journal of the American Statistical Association. pp. 1-12. ISSN 0162-1459

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Identification Number: 10.1080/01621459.2016.1188107

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.

Item Type: Article
Official URL: http://www.tandfonline.com/toc/uasa20/current
Additional Information: © 2017 American Statistical Association
Subjects: H Social Sciences > HA Statistics
Sets: Departments > Economics
Date Deposited: 12 May 2017 13:01
Last Modified: 17 Oct 2017 15:22
Projects: SNP 615882
Funders: European Research Council
URI: http://eprints.lse.ac.uk/id/eprint/76770

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