Empirical Likelihood for Random Sets

Karun Adusumilli, Taisuke Otsu

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1064-1075
Number of pages12
JournalJournal of the American Statistical Association
Volume112
Issue number519
DOIs
Publication statusPublished - 2017 Jul 3
Externally publishedYes

Fingerprint

Empirical Likelihood
Random Sets
Support Function
Tumor Growth
Brackets
Treatment Effects
Nonparametric Likelihood
Boolean Model
Medical Imaging
Image Analysis
Convex Sets
Robotics
Regression
Empirical likelihood
Tumor
Treatment effects
Inference

Keywords

  • Empirical likelihood
  • Random set
  • Treatment effect

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Empirical Likelihood for Random Sets. / Adusumilli, Karun; Otsu, Taisuke.

In: Journal of the American Statistical Association, Vol. 112, No. 519, 03.07.2017, p. 1064-1075.

Research output: Contribution to journalArticle

Adusumilli, Karun ; Otsu, Taisuke. / Empirical Likelihood for Random Sets. In: Journal of the American Statistical Association. 2017 ; Vol. 112, No. 519. pp. 1064-1075.
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