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首页> 外文会议>Information Sciences and Systems, 2009. CISS 2009 >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：比较预期和观察到的Fisher信息以获得最大似然估计的初步结果

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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（MLE）的置信区间通常用于统计推断。为了准确地构建这样的置信区间，通常需要知道MLE的分布。标准统计理论说，归一化的MLE是渐近正态的，均值零，方差是未知参数下Fisher信息矩阵（FIM）的函数。对于MLE的方差的两个常见估计是观测到的FIM（与负对数似然的Hessian相同）和预期FIM，两者均在给定样本数据的MLE上进行了评估。我们表明，在合理的条件下，在均方误差标准下，预期的FIM往往会优于观察到的FIM。该结果表明，在某些条件下，当用于置信区间计算时，预期FIM是对MLE方差的更好估计。

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