【摘要】：在統(tǒng)計學中,線性模型是一個簡單且被普遍應用的模型,它已經被廣泛應用于商業(yè)、工業(yè)以及經濟學等重要領域.在研究線性模型時,我們首先考慮的是參數估計,人們最早提出的是最小二乘估計.然而,隨著隨機變量個數的增加,最小二乘估計會出現均方誤差變大的缺陷,在各研究領域的實際問題就會出現很大偏差.為此,人們提出Bayes線性無偏最小方差估計以及一系列的有偏估計,如Stein估計、James-Stein估計、嶺估計、Liu估計等.本文研究的是線性模型中的參數估計問題,很多學者都對Bayes線性無偏最小方差估計的優(yōu)良性質進行了研究,同時也與最小二乘估計、廣義最小二乘估計、嶺估計等進行了比較.本文則在前人的研究基礎之上,討論Bayes線性無偏最小方差估計與Liu估計和James-Stein估計的關系,主要分為以下幾部分:首先在緒論中介紹線性模型的基礎知識及幾種常見估計的發(fā)展進程,其中詳細介紹了 Bayes線性無偏最小方差估計.第二章主要討論了 Bayes線性無偏最小方差估計在廣義均方誤差準則下的性質,將其與Liu估計和James-Stein估計進行比較.第三章將在平衡損失風險函數下,繼續(xù)討論Bayes線性無偏最小方差估計的性質,同樣將其與Liu估計和James-Stein估計的風險函數進行比較.
[Abstract]:In statistics, linear model is a simple and widely used model, it has been widely used in business, industry, economics and other important fields. When we study the linear model, we first consider the parameter estimation, and the least square estimation is the earliest one. However, with the increase of the number of random variables, the least square estimation will have the defect of increasing the mean square error. Therefore, Bayes linear unbiased minimum variance estimators and a series of biased estimators, such as Stein estimators, James-Stein estimators, ridge estimators, Liu estimators, are proposed. In this paper, the parameter estimation problem in linear model is studied. Many scholars have studied the excellent properties of Bayes linear unbiased minimum variance estimation, and compared it with the least square estimation, the generalized least square estimate and the ridge estimate. In this paper, on the basis of previous studies, we discuss the relationship between Bayes linear unbiased minimum variance estimator and Liu estimator and James-Stein estimator. It is mainly divided into the following parts: firstly, the basic knowledge of linear model and the development process of several common estimators are introduced in the introduction, in which the Bayes linear unbiased minimum variance estimation is introduced in detail. In chapter 2, we discuss the properties of Bayes linear unbiased least variance estimator under the generalized mean square error criterion, and compare it with Liu estimator and James-Stein estimator. In chapter 3, we continue to discuss the properties of Bayes linear unbiased minimum variance estimator under the balanced loss risk function, and compare it with the risk function of Liu estimate and James-Stein estimate.
【學位授予單位】：吉林大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212

【參考文獻】

相關期刊論文 前6條

1 劉謝進;繆柏其;;Bayes線性無偏最小方差估計相對于嶺估計的優(yōu)良性[J];華中師范大學學報(自然科學版);2013年05期

2 劉謝進;繆柏其;;平衡損失下Bayes線性無偏最小方差估計的優(yōu)良性[J];中國科學技術大學學報;2011年06期

3 劉謝進;繆柏其;;線性模型中Bayes線性無偏最小方差估計的優(yōu)良性[J];中國科學技術大學學報;2009年03期

4 霍涉云;張偉平;韋來生;;一類線性模型參數的Bayes估計及其優(yōu)良性[J];中國科學技術大學學報;2007年07期

5 劉謝進,朱允民;最優(yōu)加權最小二乘估計與線性無偏最小方差估計性能比較[J];四川大學學報(自然科學版);2001年05期

6 陳希孺;低階矩條件下線性回歸最小二乘估計弱相合的充要條件[J];中國科學(A輯 數學 物理學 天文學 技術科學);1995年04期

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