Cramer-Rao Bound for Arbitrarily Constrained Sets
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910002167414784 |
|---|---|
| author | Do, Heedong Lozano, Angel |
| author_facet | Do, Heedong Lozano, Angel |
| contents | This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher information matrix, the derived CRB applies to any constrained set and holds for any estimation bias and any Fisher information matrix. The key geometric object governing the new CRB is the tangent cone to the constraint set, whose span determines how the constraints affect the estimation accuracy. This CRB subsumes, unifies, and generalizes known special cases, offering an intuitive and broadly applicable framework to characterize the minimum mean-square error of constrained estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cramer-Rao Bound for Arbitrarily Constrained Sets Do, Heedong Lozano, Angel Signal Processing Information Theory This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher information matrix, the derived CRB applies to any constrained set and holds for any estimation bias and any Fisher information matrix. The key geometric object governing the new CRB is the tangent cone to the constraint set, whose span determines how the constraints affect the estimation accuracy. This CRB subsumes, unifies, and generalizes known special cases, offering an intuitive and broadly applicable framework to characterize the minimum mean-square error of constrained estimators. |
| title | Cramer-Rao Bound for Arbitrarily Constrained Sets |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2601.19539 |