This paper investigates the accuracy of the linear component that
forms part of an overall Hammerstein model-structure estimate, and a
key finding is that the process of estimating the non-linear element
can have a strong effect on the associated estimate of the linear
dynamics. Furthermore, this effect is not explained simply by way
of considering how the input spectrum is changed by the
non-linearity. Instead, it arises that the linear model-estimate
variability may be dominated by a term that depends on the frequency
response of the linear system itself. Amongst other things, the
main results derived here have experiment design implications for
Hammerstein system estimation.