## 线性回归中最小二乘估计的改进

Title    The improvement of least square estimation of linear    regression
Abstract
Linear regression model theory,which is rich and widely used,is an
important branch of modern statistics .One of the most basic problem is
that the estimation of regression parameters.The method has many kinds,and
the most common method is the least square estimation.However, in large
numbers of cases, least squares estimation appeared obvious drawbacks .
After many years of research by statisticians, figure out some solution
to this problem, in which the biased estimation is more commonly used
methods.
To solve the multicollinearity problem,this paper elaborates the principle
and method of some kinds of biased estimation,and compares the least
squares estimation and ridge estimate of to make a summary with the help

of SPSS software and actual data.Finally,considering the excessive
explain this problem a little ,according to the latest research results.
Keywords    linear regression,least square estimation,multicollinearity,
ridge estimation,excessive compression

1  绪论    1
1.1   多元线性回归  .  1
1.2   参数估计的发展概述  .  3
1.3   本文研究的问题  .  5
2   最小二乘估计与岭估计    7
2.1   最小二乘估计方法及性质  .  7
2.2   多重共线性问题  .  8
2.3   岭估计方法与性质  .  11
2.4   岭参数 的选择   12
3   改进效果实例研究    14
3.1   最小二乘线性回归  .  15
3.2   岭回归  .  17
4  岭估计过度压缩的改进方法    21
4.1  岭估计的主要问题  .  21
4.2  对岭估计过度压缩的改进  .  21

1  绪论
线性模型是现代统计学中理论丰富、应用广泛的一个重要分支，许多生物、医学、

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