Barankin Vector Locally Best Unbiased Estimates

06/30/2017

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by   Bruno Cernuschi-Frias, et al.

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The Barankin bound is generalized to the vector case in the mean square error sense. Necessary and sufficient conditions are obtained to achieve the lower bound. To obtain the result, a simple finite dimensional real vector valued generalization of the Riesz representation theorem for Hilbert spaces is given. The bound has the form of a linear matrix inequality where the covariances of any unbiased estimator, if these exist, are lower bounded by matrices depending only on the parametrized probability distributions.