Empirical likelihood for manifolds

Daisuke Kurisu and Taisuke Otsu

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: There has been growing interest in statistical analysis of random objects taking values in a non-Euclidean metric space. One important class of such objects consists of data on manifolds. This article is concerned with inference on the Fréchet mean and related population objects on manifolds. We develop the concept of nonparametric likelihood for data on manifolds and propose general inference methods by adapting the theory of empirical likelihood. In addition to the basic asymptotic properties, such as Wilks’ theorem of the empirical likelihood statistic, we present several generalizations of the proposed methodology: two-sample testing, inference on the Fréchet variance, quasi-Bayesian inference, local Fréchet regression, and estimation of the Fréchet mean set. Simulation and real data examples illustrate the usefulness of the proposed methodology and its advantage against the conventional Wald test.

Keywords: empirical likelihood; generalized Fréchet mean; manifold; smeariness (search for similar items in EconPapers)
JEL-codes: C1 J1 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2025-07-18
New Economics Papers: this item is included in nep-ecm
References: Add references at CitEc
Citations:

Published in Journal of the Royal Statistical Society. Series B: Statistical Methodology, 18, July, 2025. ISSN: 1369-7412

Downloads: (external link)
http://eprints.lse.ac.uk/128293/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:128293

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().