基于正态随机向量理论建构下的Fisher定理的证明  

The Proof of Fisher′s Theorem Based on Normal Random Vector Theory

作　　者：安佰玲[1] 陈书凤 夏亚玲 王国华[1] AN Bailing;CHEN Shufeng;XIA Yaling;WANG Guohua(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2022年第4期18-22,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高等学校自然科学项目(KJ2020A1200);安徽省高等学校质量工程项目(2019jyxm0201,2021jxtd257);淮北师范大学质量工程项目(2020xjxyj032,2020xjxtd004,2021xjxyj023)。

摘　　要：正态随机向量一般理论是数理统计学中基于正态总体统计推断的基础,也是Fisher定理证明的关键.本文利用n维随机变量及矩阵代数的相关理论,研究基于正态随机向量理论建构下的Fisher定理证明.该证明方法系统研究n维正态随机向量一次及二次函数的分布及独立性问题,对Fisher定理的证明进行理论建构,同时也为多元统计分析和线性回归分析的学习奠定理论基础.The theory of normal random vector is the basis of normal population statistical inference in mathe⁃matical statistics and the key to prove Fisher′s theorem.The proof of Fisher′s theorems is propsed based on the theory of n-dimensional random vector and algebra matrix.The distribution and independence of the lin⁃ear and quadratic function of n-dimensional normal random vector are systematically studied.so theoretical construction of Fisher theorem is accomplished,which lay a theoretical foundation for multivariate statistical analysis and linear regression analysis.

关 键 词：Fisher定理 n维随机向量 正态分布 概念图 

分 类 号：O212.1[理学—概率论与数理统计]