Covariance fields
| dc.creator | Balov, Nikolay H. | |
| dc.date | 2008-07-29 | |
| dc.date | 2009-01-15 | |
| dc.date.accessioned | 2026-07-07T12:29:24Z | |
| dc.date.available | 2026-07-07T12:29:24Z | |
| dc.description | We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form a covariance operator field. We show that, in most circumstances, covariance fields are continuous. We also solve the inverse problem: recovering distribution from a covariance field. Surprisingly, this is not possible on Euclidean spaces. On non-Euclidean manifolds however, covariance fields are true distribution representations. | |
| dc.description | 28 pages, core thesis paper | |
| dc.identifier | https://arxiv.org/abs/0807.4690 | |
| dc.identifier | http://arxiv.org/abs/0807.4690 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215863 | |
| dc.subject | Statistics Theory | |
| dc.subject | Differential Geometry | |
| dc.subject | Computation | |
| dc.title | Covariance fields | |
| dc.type | text |