论文标题
Fisher信息及其应用的非参数估计
Nonparametric Estimation of the Fisher Information and Its Applications
论文作者
论文摘要
本文考虑了从大小$ n $的随机样本中估算Fisher信息的问题。首先，重新审视了Bhattacharya提出的估计量，并得出了提高的收敛速率。其次，提出了一个新的估计器，称为剪切估计器。与Bhattacharya估计量相比，新估计量可以显示收敛速率上的上限，尽管具有不同的规律性条件。第三，对两个被高斯噪声污染的随机变量的实际相关情况进行了评估。此外，使用Brown的身份，将Fisher信息与高斯噪声中的最小平方误差（MMSE）相关联，提出了两个相应的MMSE一致估计器。提供了Bhattacharya估计器和剪辑估计器以及MMSE估计器的仿真示例。示例表明，与Bhattacharya估计器相比，剪切的估计器可以显着减少所需的样本量，以确保特定的置信区间。
This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new estimator, termed a clipped estimator, is proposed. Superior upper bounds on the rates of convergence can be shown for the new estimator compared to the Bhattacharya estimator, albeit with different regularity conditions. Third, both of the estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown's identity, which relates the Fisher information and the minimum mean squared error (MMSE) in Gaussian noise, two corresponding consistent estimators for the MMSE are proposed. Simulation examples for the Bhattacharya estimator and the clipped estimator as well as the MMSE estimators are presented. The examples demonstrate that the clipped estimator can significantly reduce the required sample size to guarantee a specific confidence interval compared to the Bhattacharya estimator.
