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 unbi...

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Best linear unbiased predictors developed from mixed models are widely used, but their development requires distributional assumptions or an infinite population frame...

In this paper, we derive some of the stochastic properties of a universal linear predictor, through analyses similar to those generally made in the adaptive signal processing literature. In [l], a predictor was introduced whose sequentially accumulated mean squared error for any bounded individual sequence was shown to be as small as that for any linear predictor of order less than some maximum...