Mathematics – Statistics Theory
Scientific paper
2010-10-20
Annals of Statistics 2010, Vol. 38, No. 4, 2465-2498
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS783 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/09-AOS783
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 the reconstruction of impedances of capacitors where the above scenario on the Poincar\'{e} plane exactly describes the physical system that is of statistical interest.
Huckemann Stephan F.
Kim Peter T.
Koo Ja-Yong
Munk Axel
No associations
LandOfFree
Möbius deconvolution on the hyperbolic plane with application to impedance density estimation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Möbius deconvolution on the hyperbolic plane with application to impedance density estimation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Möbius deconvolution on the hyperbolic plane with application to impedance density estimation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-717280