【摘要】：在統(tǒng)計(jì)學(xué)中,線性模型是一個(gè)簡(jiǎn)單且被普遍應(yīng)用的模型,它已經(jīng)被廣泛應(yīng)用于商業(yè)、工業(yè)以及經(jīng)濟(jì)學(xué)等重要領(lǐng)域.在研究線性模型時(shí),我們首先考慮的是參數(shù)估計(jì),人們最早提出的是最小二乘估計(jì).然而,隨著隨機(jī)變量個(gè)數(shù)的增加,最小二乘估計(jì)會(huì)出現(xiàn)均方誤差變大的缺陷,在各研究領(lǐng)域的實(shí)際問(wèn)題就會(huì)出現(xiàn)很大偏差.為此,人們提出Bayes線性無(wú)偏最小方差估計(jì)以及一系列的有偏估計(jì),如Stein估計(jì)、James-Stein估計(jì)、嶺估計(jì)、Liu估計(jì)等.本文研究的是線性模型中的參數(shù)估計(jì)問(wèn)題,很多學(xué)者都對(duì)Bayes線性無(wú)偏最小方差估計(jì)的優(yōu)良性質(zhì)進(jìn)行了研究,同時(shí)也與最小二乘估計(jì)、廣義最小二乘估計(jì)、嶺估計(jì)等進(jìn)行了比較.本文則在前人的研究基礎(chǔ)之上,討論Bayes線性無(wú)偏最小方差估計(jì)與Liu估計(jì)和James-Stein估計(jì)的關(guān)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(chǔ)知識(shí)及幾種常見(jiàn)估計(jì)的發(fā)展進(jìn)程,其中詳細(xì)介紹了 Bayes線性無(wú)偏最小方差估計(jì).第二章主要討論了 Bayes線性無(wú)偏最小方差估計(jì)在廣義均方誤差準(zhǔn)則下的性質(zhì),將其與Liu估計(jì)和James-Stein估計(jì)進(jìn)行比較.第三章將在平衡損失風(fēng)險(xiǎn)函數(shù)下,繼續(xù)討論Bayes線性無(wú)偏最小方差估計(jì)的性質(zhì),同樣將其與Liu估計(jì)和James-Stein估計(jì)的風(fēng)險(xiǎn)函數(shù)進(jìn)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(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 劉謝進(jìn);繆柏其;;Bayes線性無(wú)偏最小方差估計(jì)相對(duì)于嶺估計(jì)的優(yōu)良性[J];華中師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2013年05期

2 劉謝進(jìn);繆柏其;;平衡損失下Bayes線性無(wú)偏最小方差估計(jì)的優(yōu)良性[J];中國(guó)科學(xué)技術(shù)大學(xué)學(xué)報(bào);2011年06期

3 劉謝進(jìn);繆柏其;;線性模型中Bayes線性無(wú)偏最小方差估計(jì)的優(yōu)良性[J];中國(guó)科學(xué)技術(shù)大學(xué)學(xué)報(bào);2009年03期

4 霍涉云;張偉平;韋來(lái)生;;一類(lèi)線性模型參數(shù)的Bayes估計(jì)及其優(yōu)良性[J];中國(guó)科學(xué)技術(shù)大學(xué)學(xué)報(bào);2007年07期

5 劉謝進(jìn),朱允民;最優(yōu)加權(quán)最小二乘估計(jì)與線性無(wú)偏最小方差估計(jì)性能比較[J];四川大學(xué)學(xué)報(bào)(自然科學(xué)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(jì)弱相合的充要條件[J];中國(guó)科學(xué)(A輯 數(shù)學(xué) 物理學(xué) 天文學(xué) 技術(shù)科學(xué));1995年04期

，

本文編號(hào)：2319277