  In parameter estimation, assumptions about the model are typically considered
which allow us to build optimal estimation methods under many statistical
senses. However, it is usually the case where such models are inaccurately
known or not capturing the complexity of the observed phenomenon. A natural
question arises to whether we can find fundamental estimation bounds under
model mismatches. This paper derives a general bound on the mean square error
(MSE) following the Ziv-Zakai methodology for the widely used additive Gaussian
model. The general result accounts for erroneous functionals, hyperparameters,
and distributions differing from the Gaussian. The result is then
particularized to gain some insight into specific problems and some
illustrative examples demonstrate the predictive capabilities of the bound.
