A1018
Title: A robust estimator of location on spheres and manifolds
Authors: Jongmin Lee - Pusan National University (Korea, South) [presenting]
Sungkyu Jung - Seoul National University (Korea, South)
Abstract: The aim is to introduce Huber means on Riemannian manifolds, including circles and spheres, providing a robust alternative to the Frechet mean by integrating elements of both squared and absolute loss functions. The Huber means are designed to be highly resistant to outliers while maintaining efficiency, making it a valuable generalization of Huber's M-estimator for manifold-valued data. The statistical and computational aspects of Huber means are comprehensively investigated, demonstrating their utility in manifold-valued data analysis. Specifically, the Huber means are consistent and enjoy the central limit theorem. Additionally, a novel moment-based estimator is proposed for the limiting covariance matrix, which is used to construct a robust one-sample location test procedure and an approximate confidence region for location parameters. The Huber mean is shown to be highly robust and more efficient than the Frechet mean in the presence of outliers or under heavy-tailed distributions on spheres.
