Empirical likelihood for manifolds

• 成果类型: Article; Early Access
• 署名作者: Kurisu, Daisuke; Otsu, Taisuke
• 署名单位: University of Tokyo; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf043
• 发表日期: 2025
• 关键词: extrinsic sample means; frechet

摘要

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 Fr & eacute;chet 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 Fr & eacute;chet variance, quasi-Bayesian inference, local Fr & eacute;chet regression, and estimation of the Fr & eacute;chet mean set. Simulation and real data examples illustrate the usefulness of the proposed methodology and its advantage against the conventional Wald test.