Empirical Likelihood for Random Sets

Karun Adusumilli, Taisuke Otsu

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)1064-1075
Number of pages12
JournalJournal of the American Statistical Association
Issue number519
Publication statusPublished - 2017 Jul 3


  • Empirical likelihood
  • Random set
  • Treatment effect

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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