Deepest Minimum Criterion for Biased Affine Estimation

A new strategy called the Deepest Minimum Criterion (DMC) is presented for optimally obtaining an affine transformation of a given unbiased estimator, when a-priori information on the parameters is known. Here, it is considered that the samples are drawn from a distribution parametrized by an unknown deterministic vector parameter. The a-priori information on the true parameter vector is available in the form of a known subset of the parameter space to which the true parameter vector belongs. A closed form exact solution is given for the non-linear DMC problem in which it is known that the true parameter vector belongs to an ellipsoidal ball and the covariance matrix of the unbiased estimator does not depend on the parameters. A closed form exact solution is also given for the Min-Max strategy for this same case.