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.

翻译：针对一般模型失配下的均方误差，本文推导了一个双边（即上界和下界）界限。该界限基于χ²散度的变分表示推导得出，适用于贝叶斯和非贝叶斯框架下的有偏和无偏估计量。不同于仅依赖于模型的其他经典MSE界限，我们的界限还与估计量相关，因此可用作表征特定估计量MSE的工具。所提出的界限技术具有多种应用，其中一种应用是作为证明一类模型下估计量一致性的工具。此外，该技术揭示了某些估计量在一般模型失配条件下表现良好的原因。