关于累积量的Fisher信息
Fisher Information With Respect to Cumulants
摘要：
Fisher信息是一种最佳精确度的度量，可以从统计数据中估计参数。它也可以被定义为连续随机变量，而不参考任何参数，在这种情况下，它具有物理上令人信服的解释，表示随机变量的第一累积量，即，其平均值可以从其统计实现中估计。我们构建了一个完整的层次结构的信息措施，确定最好的精度，所有的累积量的随机变量-从而其完整的概率分布-可以估计从其统计实现。讨论了这些信息测度及其生成函数的几个性质。
英文摘要：
Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a physically compelling interpretation of representing the highest precision with which the first cumulant of the random variable, i.e., its mean, can be estimated from its statistical realizations. We construct a complete hierarchy of information measures that determine the best precision with which all of the cumulants of a random variable -- and thus its complete probability distribution -- can be estimated from its statistical realizations. Several properties of these information measures and their generating functions are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
