B1339
Title: Nonparametric inference on intrinsic means
Authors: Daisuke Kurisu - The University of Tokyo (Japan) [presenting]
Taisuke Otsu - London School of Economics (United Kingdom)
Abstract: A novel asymptotic theory is established for inference on the generalized Frechet mean using empirical likelihood (EL) methods. The focus lies in constructing confidence regions for the generalized Frechet means (such as Frechet means or Frechet medians) of manifolds. The EL statistic is demonstrated, converging to a chi-square distribution with $m$ degrees of freedom, where $m$ represents the dimension of a manifold. Importantly, this result remains robust even in the presence of smeariness. Furthermore, the versatility of the approach is explored by discussing its extensions in various directions, including two-sample testing, Bayesian quasi-inference, and nonparametric regression. To provide practical insights into the methodology, the results are seen in real data analysis as illustrations of its effectiveness.
