有偏估计及其优良准则

发布时间：2018-02-10 15:25

本文关键词： 线型回归模型 Stein型根方估计 (cM)准则岭参数　出处：《渤海大学》2017年硕士论文　论文类型：学位论文

【摘要】：线型回归模型是近代统计分析理论中非常重要一类数学模型,其基本的理论方法也成为其他统计问题研究的基本工具之一,其中参数的估计问题是很多学者们都特别关注的问题。随着对参数估计问题的不断研究,很多研究结果都表示,传统意义上的最小二乘估计在解决许多问题时,假如出现一个病态的设计矩阵,最小二乘估计就不是一个理想的估计,它的效果会变差,甚至有可能失效。因此它已经不在是一个最优的估计。因此出现了许多新型的估计量,比如岭估计,主成分估计,广义岭估计和Stein估计等等。随着研究的进一步发展,很多专家学者开始对如何对岭估计的参数更好的选择进行了深入研究,提出了多种关于选取岭参数K的方法。本文主要研究参数估计的三个问题:第一,Stein型根方估计。首先给出Stein型根方估计,给出几个定义,然后通过实际应用的例子来证明Stein型根方估计优于其他一些估计。第二,关于岭参数K的选取问题,主要介绍一些岭参数K的几种选取方法。并且对其中的岭迹法进行了实例证明。第三,(cM)准则下的泛岭估计和Stein型根方估计的性质。主要讨论的在(cM)准则下两种估计的优良性。
[Abstract]:Linear regression model is a very important mathematical model in modern statistical analysis theory. The problem of parameter estimation is of particular concern to many scholars. With the continuous study of parameter estimation, many research results indicate that the traditional least square estimation is solving many problems. If there is a sick design matrix, the least square estimation is not an ideal estimate, its effect will become worse, and it may even fail. Therefore, it is no longer an optimal estimate. For example, Ridge estimation, Principal component estimation, Generalized Ridge estimation, Stein estimation and so on. With the further development of the research, many experts and scholars have begun to do in-depth research on how to better select the parameters of ridge estimation. Several methods for selecting ridge parameter K are proposed. In this paper, three problems of parameter estimation are studied: first, Stein type root square estimation. First, the Stein type root square estimation is given, and several definitions are given. Then it is proved that the Stein type root square estimation is superior to some other estimates by practical examples. Secondly, the selection of ridge parameter K is discussed. This paper mainly introduces some methods of selecting ridge parameter K, and proves the ridge trace method as an example. The properties of panridge estimation and Stein type root square estimator under the third CMA criterion are discussed, and the advantages of the two estimators under the CMA criterion are discussed.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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