{"paper":{"title":"M\\\"{o}bius deconvolution on the hyperbolic plane with application to impedance density estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Axel Munk, Ja-Yong Koo, Peter T. Kim, Stephan F. Huckemann","submitted_at":"2010-10-20T13:49:08Z","abstract_excerpt":"In this paper we consider a novel statistical inverse problem on the Poincar\\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\\times2$ real matrices of determinant one via M\\\"{o}bius transformations. Our approach is based on a deconvolution technique which relies on the Helgason--Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random M\\\"{o}bius transform. A motivation for this work comes from "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4202","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}