Why Can Wiener-Hopf Reach Accurate Solutions With Poor Statistical Estimates?

The Wiener-Hopf solution is based on estimates of the covariance matrix and the cross-correlation vector, which will likely be poor for small sample sizes. Yet the solution can be very accurate. We explore why this is, and why it is disadvantageous to separately estimate the two statistics, or try to include explicit knowledge of the input process to the adaptive system. The results are based on a least squares interpretation of Wiener-Hopf and an exploration of the variances of estimates, which we underpin by simulations.