The optimality of linear estimation algorithms in minimax identification

The optimality of linear estimates in minimax estimation of a stochastically uncertain vector in a linear observation model by mean-square criterion is studied. In the Gaussian case, a uniformly optimal linear estimate is shown to exist in the class of all unbiased estimates. Moreover, it is minimax in the class of all nonlinear estimates if the nonrandom parameters of the observation model are unbounded. If the $a priori$ information on random parameters are given as constraints on the covariance matrix, linear estimates are shown to be minimax.