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首页> 外文会议>Annual Conference on Information Sciences and Systems >Preliminary Results in Comparing the Expected and Observed Fisher Information for Maximum Likelihood Estimates
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Preliminary Results in Comparing the Expected and Observed Fisher Information for Maximum Likelihood Estimates

机译：初步导致比较预期和观察到的Fisher信息以获得最大可能性估计

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摘要

Confidence intervals for the maximum likelihood estimates (MLEs) are commonly used in statistical inference. To accurately construct such confidence intervals, one typically needs to know the distribution of the MLE. Standard statistical theory says normalized MLE is asymptotically normal with mean zero and variance being a function of the Fisher Information Matrix (FIM) at the unknown parameter. Two common estimates for the variance of MLE are the observed FIM (same as Hessian of negative log-likelihood) and the expected FIM, both of which are evaluated at the MLE given sample data. We show that, under reasonable conditions, the expected FIM tends to outperform 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 variance of MLE when used in confidence interval calculations.
机译：最大似然估计（MLES）的置信区间通常用于统计推理。为了准确地构造这种置信区间，通常需要知道MLE的分布。标准统计理论称，归一化MLE是渐近的渐近正常，其平均零和方差是未知参数的Fisher信息矩阵（FIM）的函数。对于MLE方差的两个常见估计是观察到的FIM（与阴性日志似然相同）和预期的FIM，两者在给定的样本数据时评估。我们表明，在合理的条件下，预期的FIM倾向于在平均平均误差标准下倾向于观察到的FIM。该结果表明，在某些条件下，预期的FIM是在置信区间计算中使用时MLE的差异更好地估计。

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