Preliminary results on relative performance of expected and observed fisher information
Preliminary results on relative performance of expected and observed fisher information
复制标题
预期和观察到的渔民信息相对表现的初步结果
DOI：
10.1109/cdc.2009.5400435
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Spall
中科院分区：
文献类型：
--
作者：
Xumeng Cao;J. Spall
最大似然估计（MLE）的协方差计算和置信区间通常用于识别和统计推断。为了准确地构造这样的置信区间，通常需要知道MLE的协方差。标准统计理论表明，标准化MLE是渐近正态分布的，均值为零，协方差是未知参数下Fisher信息矩阵（Fisher Information Matrix）的倒数。最大似然估计的协方差的两个常见估计是观测到的最大似然的倒数（与负对数似然的Hessian相同）和期望最大似然的倒数（与Hessian相同）：这两个估计都是在样本数据的最大似然估计中进行的。我们表明，在合理的条件下，预期的预测优于观察到的预测下的均方误差准则。这一结果表明，在某些条件下，当用于置信区间计算时，期望的最大似然估计是MLE协方差的更好估计。
Covariance calculations and confidence intervals for maximum likelihood estimates (MLEs) are commonly used in identification and statistical inference. To accurately construct such confidence intervals, one typically needs to know the covariance of the MLE. Standard statistical theory shows that the normalized MLE is asymptotically normally distributed with mean zero and covariance being the inverse of the Fisher Information Matrix (FIM) at the unknown parameter. Two common estimates for the covariance of MLE are the inverse of the observed FIM (the same as the Hessian of negative loglikelihood) and the inverse of the expected FIM (the same as FIM): both of which are evaluated at the MLE from the sample data. We show that, under reasonable conditions, the expected FIM outperforms the observed FIM under a mean-squared error criterion. This result suggests that, under certain conditions, the expected FIM is a better estimate for the covariance of MLE when used in confidence interval calculations.