Finite-sample bounds on the accuracy of Bhattacharya’s plug-in estimator for Fisher information are derived. These bounds are further improved by introducing a clipping step that allows for better control over the score function. This leads to superior upper bounds on the rates of convergence, albeit under slightly different regularity conditions. The performance bounds on both estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown’s identity, two corresponding estimators of the minimum mean-square error are proposed.

中文翻译：

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Fisher信息的插入式估计器精度的有限样本界

推导了Bhattacharya的Fisher信息估计器精度的有限样本范围。通过引入裁剪步骤可以更好地控制得分功能，从而进一步改善了这些界限。即使在规律性条件稍有不同的情况下，这也会导致收敛速率的上限更高。针对高斯噪声污染的随机变量的实际相关情况，评估了两个估计器的性能范围。此外，利用布朗恒等式，提出了两个相应的最小均方误差估计器。