Maximum likelihood estimates and corresponding confidence regions of the estimates are commonly used in statistical inference. In practice, people often construct approximate confidence regions with the Fisher information at given sample data based on the asymptotic normal distribution of the MLE (maximum likelihood estimate). Two common Fisher information matrices (FIMs, for multivariate parameters) are the observed FIM (the Hessian matrix of negative log-likelihood function) and the expected FIM (the expectation of the observed FIM). In this article, we prove that under certain conditions and with an MSE (mean-squared error) criterion, approximate confidence interval of each element of the MLE with the expected FIM is at least as accurate as that with the observed FIM.

翻译：在统计推论中通常使用估计数的最大可能性和相应的信任区,在实际中,人们往往根据渔业部的无症状正常分布(最大可能性估计),根据特定样本数据,以渔业部门的信息建立大致的信任区,两种常见的渔业信息矩阵(多变量参数的FIM)是观察到的FIM(负日志相似函数的赫西安矩阵)和预期FIM(观察到的FIM的预期值),在本条中,我们证明,在某些条件下,根据MSE(中度误差)标准,与预期FIM的每个要素的大致信任区间至少与观察到的FIM的相同。