  Reduced-rank approach has been used for decades in robust linear estimation
of both deterministic and random vector of parameters in linear model
y=Hx+\sqrt{epsilon}n. In practical settings, estimation is frequently performed
under incomplete or inexact model knowledge, which in the stochastic case
significantly increases mean-square-error (MSE) of an estimate obtained by the
linear minimum mean-square-error (MMSE) estimator, which is MSE-optimal among
linear estimators in the theoretical case of perfect model knowledge. However,
the improved performance of reduced-rank estimators over MMSE estimator in
estimation under incomplete or inexact model knowledge has been established to
date only by means of numerical simulations and arguments indicating that the
reduced-rank approach may provide improved performance over MMSE estimator in
certain settings. In this paper we focus on the high signal-to-noise ratio
(SNR) case, which has not been previously considered as a natural area of
application of reduced-rank estimators. We first show explicit sufficient
conditions under which familiar reduced-rank MMSE and truncated SVD estimators
achieve lower MSE than MMSE estimator if singular values of array response
matrix H are perturbed. We then extend these results to the case of a generic
perturbation of array response matrix H, and demonstrate why MMSE estimator
frequently attains higher MSE than reduced-rank MMSE and truncated SVD
estimators if H is ill-conditioned. The main results of this paper are verified
in numerical simulations.
