We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct explicit representations for the score functions. 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. The case of the sums of independent random variables are discussed as well.

翻译：我们为研究非线性统计的中央限值理论中的渔业信息距离制定了一种一般方法,我们首先为得分函数建立明确的表述方式,然后利用这些表述方式得出渔业信息距离的量化估计,为说明我们方法的适用性,提供了渔业信息在二次形式上的明确趋同率和抽样手段的功能,并讨论了独立随机变量的总和。