Abstract It is shown that both the classic and the Bayesian Cramer–Rao bounds can be obtained by minimizing the mean square error of an estimator while constraining the underlying distribution to be within a Fisher information ball. The presented results allow for some nonstandard interpretations of the Cramer–Rao bound and, more importantly, provide a template for novel bounds on the accuracy of estimators.

中文翻译：

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Cramer-Rao 界的变分解释

摘要 结果表明，经典和贝叶斯 Cramer-Rao 边界都可以通过最小化估计量的均方误差同时将基础分布限制在 Fisher 信息球内来获得。所呈现的结果允许对 Cramer-Rao 界限进行一些非标准解释，更重要的是，为估计量的准确性提供了新界限的模板。