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极大似然估计的渐近正态性(MLAN)是数理统计中最著名和最基本的结果之一，MLAN的界是一个重要的热点研究课题。研究了二维正态分布的MLAN的界，在较简单的条件下，得到了极大似然估计函数的期望与正态变量函数的期望之差的界。由此得到了二维标准正态分布中相关系数的MLAN的界。与现有文献的结论相比，优势在于分布的维数从一维到二维(也有文献考虑多维，但不是正态分布)，条件易于满足，结论简洁。
Abstract：The asymptotic normality of maximum likelihood estimators( MLAN) is one of the most well-known and fundamental results in mathematical statistics,and the boundary of MLAN is a hot research topic. This study explores the bounds of MLAN with two-dimensional normal distribution and obtains the bounds of the expected difference between the function of maximum likelihood estimator and function of normal random variable under relatively simple conditions. Thus,it obtains the boundary of the MLAN for the correlation coefficient in the two-dimensional standard normal distribution.Compared with the conclusions of existing references,our advantage lies in the fact that the distribution ranges from one to two dimensions( some references also considers multiple dimensions,but not normal distribution),the conditions are easy to satisfy,and the conclusions are concise.
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基本信息:
中图分类号:O212.1
引用信息:
[1]胡宏昌,董浩,云天行.二维正态分布的极大似然估计的渐近正态性的界[J].湖北师范大学学报(自然科学版),2026,46(01):24-30.
基金信息:
湖北省自然科学基金(2025AFC080)
2025-07-14
2025
2025-11-03
2025
1
2025-12-04
2025-12-04
2025-12-04