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Geodesic lower bound for parametric estimation with constraints

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2 Author(s)
J. Xavier ; Inst. Superior Tecnico, Lisboa, Portugal ; V. Barroso

We consider parametric statistical models indexed by embedded submanifolds ⊗ of Rp. This setup occurs in practical applications whenever the parameter of interest θ is known to satisfy a priori deterministic constraints, encoded herein by ⊗. We assume that the submanifold ⊗ is connected and endowed with the Riemannian structure inherited from the ambient space Rp. This turns ⊗ into a metric space in which the distance between points corresponds to the geodesic distance. We discuss a lower bound for the intrinsic variance (that is, measured in terms of the geodesic distance) of unbiased estimators taking values in ⊗. A numerical example involving the special group of orthogonal matrices SO(n, R) is worked out.

Published in:

Signal Processing Advances in Wireless Communications, 2004 IEEE 5th Workshop on

Date of Conference:

11-14 July 2004