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  本文選題：Bayes預(yù)測　切入點(diǎn)：參數(shù)型經(jīng)驗Bayes預(yù)測　出處：《東華理工大學(xué)》2017年碩士論文

【摘要】：本文研究了有限正態(tài)總體中線性數(shù)量和二次型數(shù)量的貝葉斯預(yù)測問題及總體總量的經(jīng)驗Bayes預(yù)測問題.第一章,介紹了有限總體模型及其預(yù)測問題的研究進(jìn)展,Bayes方法原理和經(jīng)驗Bayes方法,以及本文的研究意義和結(jié)構(gòu)安排.第二章,主要研究了有限總體中線性數(shù)量和二次型數(shù)量的貝葉斯預(yù)測.首先,在正態(tài)-逆伽瑪先驗和無信息先驗下,本文分別給出了總體數(shù)量的Bayes預(yù)測;其次,本文進(jìn)一步研究線性數(shù)量和二次型數(shù)量的貝葉斯預(yù)測并得到了它們的Bayes預(yù)測風(fēng)險;最后,本文給出了幾個實(shí)例來闡明研究的結(jié)果.第三章,主要研究了有限正態(tài)總體中總體總量的經(jīng)驗貝葉斯預(yù)測.首先,基于貝葉斯思想得到了總體總量的貝葉斯預(yù)測;其次,考慮到該貝葉斯預(yù)測中存在冗余參數(shù),在實(shí)際應(yīng)用中不可行,為此利用歷史樣本構(gòu)造了總體總量的參數(shù)型經(jīng)驗Bayes預(yù)測(PEBP);最后,在均方誤差準(zhǔn)則下,討論了總體總量的的PEBP相對于最佳線性無偏預(yù)測(BLUP)的優(yōu)良性.
[Abstract]:In this paper, we study the Bayesian prediction problem of linear quantity and quadratic quantity in finite normal population and the empirical Bayes prediction problem of total population. This paper introduces the research progress of finite population model and its prediction problem. The principle of Bayesian method and empirical Bayes method are introduced, as well as the significance and structure of this paper. This paper mainly studies Bayesian prediction of linear quantity and quadratic quantity in finite population. Firstly, under the condition of normal-inverse gamma priori and no information priori, the Bayes prediction of the total quantity is given respectively. In this paper, we further study the Bayesian prediction of linear quantity and quadratic quantity and obtain their Bayes prediction risks. Finally, we give several examples to illustrate the results of the study. This paper mainly studies the empirical Bayesian prediction of the total population in the finite normal population. Firstly, the Bayesian prediction of the total amount is obtained based on the Bayesian theory; secondly, considering the redundant parameters in the Bayesian prediction, It is not feasible in practical application. For this reason, the parametric empirical Bayes prediction of total population is constructed by using historical samples. Finally, under the mean square error criterion, the superiority of the PEBP of the total population relative to the optimal linear unbiased prediction is discussed.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.8

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本文編號：1682976