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多元线性回归的参数估计方法

发表时间:2009-01-15  浏览量:2536  下载量:1094
全部作者: 吴仕勋,赵东方,金秀云
作者单位: 华中师范大学数学与统计学学院
摘 要: 多元线性回归模型是用来表示一种现象与另外多种现象之间的依存关系,对其参数的估计有很多方法,比如最小二乘估计方法、最大似然估计等。本文依据高斯-马尔可夫定理,通过对最小二乘估计方法得出的参数估计值的分析,利用矩阵分解的方法得出了另外一种估计方法。另外,从估计量的方差最小角度出发得出的估计量与最小二乘估计方法得出的估计量是一样的,且方差是所有线性估计量中最小的。
关 键 词: 概率论与数理统计;最小二乘法;参数估计;线性
Title: The parameter estimation method of multi-dimensional linear regression
Author: WU Shixun, ZHAO Dongfang, JIN Xiuyun
Organization: School of Mathematics and Statistics, Huazhong Normal University
Abstract: Multiple linear regression model is used to show the dependent relationship between a kind of phenomenon and a variety of other phenomena. There are a lot of ways to estimate the parameters, such as the least square estimation method, the maximum likelihood estimation and so on. According to the Gauss-Markov theorem, through the analysis of parameter estimation value from the least square estimation method, this paper uses matrix decomposition method to get another estimation method, and gets the same estimator as the least square method from the minimum variance of the estimation. Moreover, the variance is the smallest of all the linear estimation.
Key words: probability theory and mathematical statistics; least square method; parameter estimation; linear
发表期数: 2009年1月第1期
引用格式: 吴仕勋,赵东方,金秀云. 多元线性回归的参数估计方法[J]. 中国科技论文在线精品论文,2009,2(1):68-72.
 
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