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Content Provider | IEEE Xplore Digital Library |
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Author | Xavier, J. Barroso, V. |
Copyright Year | 2005 |
Description | Author affiliation: Inst. de Sistemas a Robotica, Inst. Superior Tecnico, Lisboa, Portugal (Xavier, J.; Barroso, V.) |
Abstract | We consider parametric statistical models in which the parameter space /spl theta/ is a connected Riemannian manifold. This mathematical structure on the parameter space subsumes, as special cases, submanifolds of Euclidean spaces appearing in parametric estimation scenarios with a priori smooth deterministic constraints, and quotient spaces (such as Grassmann manifolds) which arise in certain parametric estimation scenarios with ambiguities. The Riemannian structure on the parameter space /spl theta/ turns it into a metric space and the associated Riemannian distance is used here to quantify estimation errors. We present the intrinsic variance lower bound (IVLB) which places a lower limit on the accuracy, measured in terms of the mean-square Riemannian distance, of unbiased estimators taking values in /spl theta/. The IVLB depends both on the curvature of the parameter space and a coordinate-free extension of the well-known Fisher information matrix (FIN). We show that for flat Euclidean spaces, the IVLB collapses to the Cramer-Rao bound (CRB). In this sense, we may interpret the IVLB as a generalization of the CRB for curved parameter spaces. Computer simulations illustrating the application of the IVLB are included. |
Sponsorship | IEEE Signal Processing Soc |
File Size | 320729 |
File Format | |
ISBN | 0780388747 |
ISSN | 15206149 |
DOI | 10.1109/ICASSP.2005.1416483 |
Language | English |
Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher Date | 2005-03-23 |
Publisher Place | USA |
Access Restriction | Subscribed |
Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subject Keyword | Cramer-Rao bounds Estimation error Computer simulation Application software Probability density function Density measurement Ellipsoids Parametric statistics Quantum cellular automata Contracts |
Content Type | Text |
Resource Type | Article |
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