本文選題：異方差　切入點：套設計模型　出處：《北方工業(yè)大學》2014年碩士論文　論文類型：學位論文

【摘要】：統(tǒng)計模型中一種重要的模型就是混合效應模型,該模型可廣泛應用于生物統(tǒng)計、經(jīng)濟管理、醫(yī)療案例分析等重要的前沿領域。其中混合模型中固定效應以及隨機效應的顯著性檢驗一直是統(tǒng)計學家研究的重點。而套設計模型作為一種特殊的混合效應模型,通常是由于社會的分級結構、數(shù)據(jù)的重復測量以及含個體效應和時間效應的經(jīng)濟問題等原因而產(chǎn)生的；其廣泛應用于多層統(tǒng)計分析中,并在區(qū)域經(jīng)濟調(diào)查和計量經(jīng)濟學等領域也經(jīng)常被用到。因此,在套設計模型中有關固定效應和隨機效應的顯著性檢驗問題也至關重要。本文主要對在異方差下兩級套設計模型中的固定效應以及隨機效應的顯著性進行檢驗,并且也對異方差下一般混合效應模型中方差分量的檢驗問題進行了分析。 本文的研究內(nèi)容包括以下兩個方面： 1.研究了在異方差下兩級套設計模型中主效應和隨機效應的存在性問題。針對主效應的檢驗,提出了一種PB檢驗方法,并將其與已存在的GF檢驗進行比較,用MC模擬兩種檢驗方法犯第一類錯誤的概率。我們的研究表明：PB檢驗比GF檢驗更加優(yōu)越。盡管在小樣本模型中,GF檢驗、PB檢驗都具有令人滿意的結果,但當因子組合數(shù)或者處理組的數(shù)量增加時,GF檢驗會有比較嚴重的第一類錯誤。我們的研究還表明：有關兩級套設計模型中隨機套效應的方差分量是否為零的檢驗,該方法同樣適用。 2.對異方差下兩級套設計模型的隨機套效應方差分量是否小于等于某個給定的正數(shù)進行檢驗。利用重抽樣的思想,提出了一種PB檢驗方法,并將其與己存在的GF檢驗進行比較,用MC方法模擬兩個檢驗方法犯第一類錯誤的概率。研究表明：此時PB檢驗有比較好的檢驗效果。本文還對一般混合效應模型中的設計矩陣進行譜分解,在此基礎上,給出一種PB檢驗方法,并利用MC方法模擬其犯第一類錯誤的概率。
[Abstract]:One of the most important models in statistical models is the mixed effect model, which can be widely used in biological statistics, economic management, Medical case analysis and other important frontier fields. Among them, the significance test of fixed effect and random effect in mixed model has been the focus of statisticians. As a special mixed effect model, the set design model is a special hybrid effect model. It is usually caused by the hierarchical structure of society, repeated measurements of data, and economic problems with individual and time effects; it is widely used in multilayer statistical analysis. And is often used in areas such as regional economic surveys and econometrics. It is also very important to test the significance of fixed effect and random effect in jacket design model. This paper mainly tests the significance of fixed effect and random effect in two-stage jacket design model under heteroscedasticity. The test problem of variance component in general mixed effect model under heteroscedasticity is also analyzed. The research content of this paper includes the following two aspects:. 1. The existence of main effect and random effect in two-stage jacket design model under heteroscedasticity is studied. A PB test method is proposed for the test of principal effect and compared with the existing GF test. Using MC to simulate the probability of making the first error in two test methods. Our study shows that the w PB test is superior to the GF test. However, when the number of factor combinations or the number of treatment groups increases, there will be serious errors in the first class of the GF test. Our study also shows that the test of whether the variance component of the random sleeve effect in the two-stage sleeve design model is zero or not. The method is also applicable. 2. To test whether the variance component of random sleeve effect of two-stage jacket design model under heteroscedasticity is less than or equal to a given positive number, a PB test method is proposed by using the idea of re-sampling, and compared with the existing GF test. MC method is used to simulate the probability of two test methods making the first kind of error. The results show that PB test has better test effect at this time. In this paper, the design matrix in general mixed effect model is decomposed by spectrum, and on this basis, In this paper, a PB test method is presented, and the probability of making the first kind of mistake is simulated by MC method.
【學位授予單位】：北方工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：O212.1

【參考文獻】

相關期刊論文 前1條

1 史建紅,王松桂;方差分量的廣義譜分解估計[J];高校應用數(shù)學學報A輯(中文版);2005年01期

，

本文編號：1568632