A Bayesian approach to the estimation of maps between riemannian manifolds
| dc.creator | Butler, Leo T. | |
| dc.creator | Levit, Boris | |
| dc.date | 2007-05-17 | |
| dc.date | 2008-03-25 | |
| dc.date.accessioned | 2026-07-07T09:27:57Z | |
| dc.date.available | 2026-07-07T09:27:57Z | |
| dc.description | Let Θbe a smooth compact oriented manifold without boundary, embedded in a euclidean space and let γbe a smooth map Θinto a riemannian manifold Λ. An unknown state θ\in Θis observed via X=θ+εξwhere ε>0 is a small parameter and ξis a white Gaussian noise. For a given smooth prior on Θand smooth estimator g of the map γwe derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces Θand Λ, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of γis found based on the modern theory of harmonic maps and hypo-elliptic differential operators. | |
| dc.description | 20 pages, no figures published version includes correction to eq.s 31, 41, 43 | |
| dc.identifier | https://arxiv.org/abs/0705.2540 | |
| dc.identifier | http://arxiv.org/abs/0705.2540 | |
| dc.identifier | Mathematical Methods of Statistics. 16(4):1--17, 2007 | |
| dc.identifier | doi:10.3103/S1066530707040011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157287 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62C10, 62C20 | |
| dc.title | A Bayesian approach to the estimation of maps between riemannian manifolds | |
| dc.type | text |