A simple derivation of the constrained multiple parameter Cramer-Rao bound

J.D. Gorman and A.O. Hero (1988) obtained a remarkable extension to the classical multiple parameter Cramer-Rao (CR) lower bound that accounts for deterministic nonlinear equality constraints on the parameters. The virtue of Gorman and Hero's result is that the constrained CR bound on all of the parameters is obtained by subtracting an easily computed nonnegative definite correction matrix from the unconstrained CR bound matrix. The author presents a new, simple derivation of the constrained CR bound and a new necessary condition for an estimator to satisfy the constrained CR bound with equality.<
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