MOBIUS DECONVOLUTION ON THE HYPERBOLIC PLANE WITH APPLICATION TO IMPEDANCE DENSITY ESTIMATION
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Huckemann, Stephan F. | - |
dc.contributor.author | Kim, Peter T. | - |
dc.contributor.author | Koo, Ja-Yong | - |
dc.contributor.author | Munk, Axel | - |
dc.date.accessioned | 2021-09-08T01:25:16Z | - |
dc.date.available | 2021-09-08T01:25:16Z | - |
dc.date.created | 2021-06-14 | - |
dc.date.issued | 2010-08 | - |
dc.identifier.issn | 0090-5364 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/116022 | - |
dc.description.abstract | In this paper we consider a novel statistical inverse problem on the Poincare, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of 2 x 2 real matrices of determinant one via Mobius 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 Mains transform. A motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the Poincare plane exactly describes the physical system that is of statistical interest. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | INST MATHEMATICAL STATISTICS | - |
dc.subject | STATISTICAL INVERSE PROBLEMS | - |
dc.subject | EXTRINSIC SAMPLE MEANS | - |
dc.subject | PARAMETER | - |
dc.subject | SELECTION | - |
dc.subject | REGULARIZATION | - |
dc.subject | CONVERGENCE | - |
dc.subject | MANIFOLDS | - |
dc.subject | RATES | - |
dc.title | MOBIUS DECONVOLUTION ON THE HYPERBOLIC PLANE WITH APPLICATION TO IMPEDANCE DENSITY ESTIMATION | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Koo, Ja-Yong | - |
dc.identifier.doi | 10.1214/09-AOS783 | - |
dc.identifier.scopusid | 2-s2.0-77955159363 | - |
dc.identifier.wosid | 000280359400017 | - |
dc.identifier.bibliographicCitation | ANNALS OF STATISTICS, v.38, no.4, pp.2465 - 2498 | - |
dc.relation.isPartOf | ANNALS OF STATISTICS | - |
dc.citation.title | ANNALS OF STATISTICS | - |
dc.citation.volume | 38 | - |
dc.citation.number | 4 | - |
dc.citation.startPage | 2465 | - |
dc.citation.endPage | 2498 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.subject.keywordPlus | STATISTICAL INVERSE PROBLEMS | - |
dc.subject.keywordPlus | EXTRINSIC SAMPLE MEANS | - |
dc.subject.keywordPlus | PARAMETER | - |
dc.subject.keywordPlus | SELECTION | - |
dc.subject.keywordPlus | REGULARIZATION | - |
dc.subject.keywordPlus | CONVERGENCE | - |
dc.subject.keywordPlus | MANIFOLDS | - |
dc.subject.keywordPlus | RATES | - |
dc.subject.keywordAuthor | Cayley transform | - |
dc.subject.keywordAuthor | cross-validation | - |
dc.subject.keywordAuthor | deconvolution | - |
dc.subject.keywordAuthor | Fourier analysis | - |
dc.subject.keywordAuthor | Helgason-Fourier transform | - |
dc.subject.keywordAuthor | hyperbolic space | - |
dc.subject.keywordAuthor | impedance | - |
dc.subject.keywordAuthor | Laplace-Beltrami operator | - |
dc.subject.keywordAuthor | Mobius transformation | - |
dc.subject.keywordAuthor | special linear group | - |
dc.subject.keywordAuthor | statistical inverse problems | - |
dc.subject.keywordAuthor | upper half-plane | - |
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