A1226
Title: Empirical likelihood for manifolds
Authors: Daisuke Kurisu - The University of Tokyo (Japan) [presenting]
Taisuke Otsu - London School of Economics (United Kingdom)
Abstract: Inference for the Frechet mean and related population objects on Riemannian manifolds is investigated. A notion of nonparametric likelihood for data taking values on manifolds is developed and a general inference framework based on empirical likelihood theory is proposed. Beyond establishing fundamental asymptotic results, such as a Wilks-type theorem for the empirical likelihood statistic, several extensions of the proposed methodology are presented, including two-sample testing, inference for the Frechet variance, quasi-Bayesian inference, local Frechet regression, and estimation of the Frechet mean set. The practical performance of the approach is demonstrated through numerical experiments and three real data applications: inference for the Frechet mean and median of turtle movement direction data and virtual geomagnetic pole direction data, and a two-sample test for the Frechet mean and median of mouse thoracic vertebra shape data. These results highlight the effectiveness of the proposed methods and their advantages over conventional Wald procedures.
