Why the stochastic MV-PURE estimator excels in highly noisy situations?

The stochastic MV-PURE estimator has recently emerged as the robust solution for frequently occuring in practice problem of linear estimation in ill-conditioned and imperfectly known linear stochastic model. In this paper we provide theoretical results showing that the stochastic MV-PURE estimator can be used to the greatest effect in highly noisy settings. In such settings, we discuss the relation between the stochastic MV-PURE estimator and the well-known reduced rankWiener filter. We verify the theoretical results presented by a means of numerical simulations.