• • 上一篇    下一篇

统一精度指标及与香农定理的联系

刘亚文1,马文博2,杜子芳2   

  1. 1. 对外经济贸易大学统计学院, 北京 100029;2. 中国人民大学统计学院,北京 100872
  • 出版日期:2021-12-28 发布日期:2021-12-28

刘亚文, 马文博, 杜子芳. 统一精度指标及与香农定理的联系[J]. 系统科学与数学, 2022, 42(1): 64-71.

LIU Yawen, MA Wenbo, DU Zifang. Unified Precision Measure and Its Relationship with Shannon's Theorem[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(1): 64-71.

Unified Precision Measure and Its Relationship with Shannon's Theorem

LIU Yawen1, MA Wenbo2 ,DU Zifang2   

  1. 1. School of Statistics, University of International Business and Economics, Beijing 100029; 2. School of Statistics, Renmin University of China, Beijing 100872
  • Online:2021-12-28 Published:2021-12-28
统计推断通常以置信度和误差两个指标衡量估计精度,但当置 信度和误差其大小均不同时,估计量之间的精度比较将十分困难.文章 提出了一个可广泛使用的无量纲精度指标,当估计误差不一,置信度也 不一时,也能够进行精度比较.另从解释精度影响因素及其作用机制出发,发 现了样本量确定公式与信息论之香农定理的逻辑一致性,并借此给出了关于样本量确定公式物理意义的一个新视角下的解释.
Statistical inference usually measures the estimation accuracy by two indicators: Confidence coefficient and bias, but when confidence coefficient and bias are different, the comparison of accuracy between estimators will be difficult. In this paper, a widely used dimensionless accuracy statistic is proposed. The function of confidence coefficient and bias can compare the accuracy when the estimation bias and the degree of confidence are different at the same time. In addition, starting from the factors affecting the interpretation accuracy and its action mechanism, the logical consistency between the sample size determination formula and the Shannon theorem of information theory is found. A new explanation of the physical meaning of the sample size determination formula is given.
()
No related articles found!
阅读次数
全文


摘要