热统计学的几个基本元素
1Department of Mathematics and Statistics, UNC Charlotte, Charlotte, NC 28223, USA.
Entropy (Basel, Switzerland)
|July 29, 2023
概括
这项研究引入了统计学,超越了传统的随机变量,分析了字母表上的一般随机元素. 它为基于的统计方法建立了理论框架,增强了数据科学推断.
科学领域:
- 统计 统计 统计 统计
- 数据科学数据科学数据科学
- 信息理论 信息理论
背景情况:
- 现代数据科学正在将统计推理从传统的随机变量转移到基于字母表的更一般的随机元素.
- 现有的统计理论对于随机变量来说已经发展得很好,但对于对字母表的推理,特别是估计来说,系统性较差.
- 随机元素的邻近和时刻等熟悉的概念的缺失需要基于的统计学新的理论基础.
研究的目的:
- 介绍和讨论统计的基本元素.
- 开发一个严格的理论框架,用于基于一般随机元素和的统计推理.
- 将现有的统计定理扩展到域.
主要方法:
- 介绍一般的,样空间,分布和统计.
- 一个产生势的函数的定义.
- 建立了格利文科 - 坎特利收定理的缩版本.
主要成果:
- 定义和讨论了统计学的几个基本对象.
- 演示了热时刻生成函数从热角度独特地表征分布.
- 建立了Glivenko-Cantelli的热定理,提供了一个趋同保证.
结论:
- 该研究为热统计学提供了健全的理论框架奠定了基础.
- 开发的学工具和定理使得涉及一般随机元素和的更严格的统计练习成为可能.
- 这项工作弥合了数据科学中传统统计和信息理论方法之间的差距.
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