论文标题
非线性统计中心限制定理中的Fisher信息收敛速率
Rates of Fisher information convergence in the central limit theorem for nonlinear statistics
论文作者
论文摘要
我们开发了一种一般方法，以研究非线性统计的中央限制定理中的Fisher信息距离。我们首先为分数函数构建全新表示。然后，我们使用这些表示形式来得出Fisher信息距离的定量估计。为了说明我们方法的适用性，提供了二次形式的Fisher信息收敛速率以及样本平均值的功能。对于独立随机变量的总和，我们获得了Fisher信息界限，而无需庞加莱常数的有限。我们的方法还可以用来以非中心极限定理的方式绑定Fisher信息距离。
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random variables, we obtain the Fisher information bounds without requiring the finiteness of Poincaré constant. Our method can also be used to bound the Fisher information distance in non-central limit theorems.
