{"ID":2843873,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06933","arxiv_id":"2511.06933","title":"Transformed Fréchet Means for Robust Estimation in Hadamard Spaces","abstract":"We establish finite-sample error bounds in expectation for transformed Fréchet means in Hadamard spaces under minimal assumptions. Transformed Fréchet means provide a unifying framework encompassing classical and robust notions of central tendency in metric spaces. Instead of minimizing squared distances as for the classical 2-Fréchet mean, we consider transformations of the distance that are nondecreasing, convex, and have a concave derivative. This class spans a continuum between median and classical mean. It includes the Fréchet median, power Fréchet means, and the (pseudo-)Huber mean, among others. We obtain the parametric rate of convergence under fewer than two moments and a subclass of estimators exhibits a breakdown point of 1/2. Our results apply in general Hadamard spaces-including infinite-dimensional Hilbert spaces and nonpositively curved geometries-and yield new insights even in Euclidean settings.","short_abstract":"We establish finite-sample error bounds in expectation for transformed Fréchet means in Hadamard spaces under minimal assumptions. Transformed Fréchet means provide a unifying framework encompassing classical and robust notions of central tendency in metric spaces. Instead of minimizing squared distances as for the cla...","url_abs":"https://arxiv.org/abs/2511.06933","url_pdf":"https://arxiv.org/pdf/2511.06933v1","authors":"[\"Christof Schötz\"]","published":"2025-11-10T10:27:15Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}