  A bilateral (i.e., upper and lower) bound on the mean-square error under a
general model mismatch is developed. The bound, which is derived from the
variational representation of the chi-square divergence, is applicable in the
Bayesian and nonBayesian frameworks to biased and unbiased estimators. Unlike
other classical MSE bounds that depend only on the model, our bound is also
estimator-dependent. Thus, it is applicable as a tool for characterizing the
MSE of a specific estimator. The proposed bounding technique has a variety of
applications, one of which is a tool for proving the consistency of estimators
for a class of models. Furthermore, it provides insight as to why certain
estimators work well under general model mismatch conditions.
