本文選題：異方差　切入點(diǎn)：套設(shè)計(jì)模型　出處：《北方工業(yè)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：統(tǒng)計(jì)模型中一種重要的模型就是混合效應(yīng)模型,該模型可廣泛應(yīng)用于生物統(tǒng)計(jì)、經(jīng)濟(jì)管理、醫(yī)療案例分析等重要的前沿領(lǐng)域。其中混合模型中固定效應(yīng)以及隨機(jī)效應(yīng)的顯著性檢驗(yàn)一直是統(tǒng)計(jì)學(xué)家研究的重點(diǎn)。而套設(shè)計(jì)模型作為一種特殊的混合效應(yīng)模型,通常是由于社會(huì)的分級(jí)結(jié)構(gòu)、數(shù)據(jù)的重復(fù)測量以及含個(gè)體效應(yīng)和時(shí)間效應(yīng)的經(jīng)濟(jì)問題等原因而產(chǎn)生的；其廣泛應(yīng)用于多層統(tǒng)計(jì)分析中,并在區(qū)域經(jīng)濟(jì)調(diào)查和計(jì)量經(jīng)濟(jì)學(xué)等領(lǐng)域也經(jīng)常被用到。因此,在套設(shè)計(jì)模型中有關(guān)固定效應(yīng)和隨機(jī)效應(yīng)的顯著性檢驗(yàn)問題也至關(guān)重要。本文主要對(duì)在異方差下兩級(jí)套設(shè)計(jì)模型中的固定效應(yīng)以及隨機(jī)效應(yīng)的顯著性進(jìn)行檢驗(yàn),并且也對(duì)異方差下一般混合效應(yīng)模型中方差分量的檢驗(yàn)問題進(jìn)行了分析。 本文的研究內(nèi)容包括以下兩個(gè)方面： 1.研究了在異方差下兩級(jí)套設(shè)計(jì)模型中主效應(yīng)和隨機(jī)效應(yīng)的存在性問題。針對(duì)主效應(yīng)的檢驗(yàn),提出了一種PB檢驗(yàn)方法,并將其與已存在的GF檢驗(yàn)進(jìn)行比較,用MC模擬兩種檢驗(yàn)方法犯第一類錯(cuò)誤的概率。我們的研究表明：PB檢驗(yàn)比GF檢驗(yàn)更加優(yōu)越。盡管在小樣本模型中,GF檢驗(yàn)、PB檢驗(yàn)都具有令人滿意的結(jié)果,但當(dāng)因子組合數(shù)或者處理組的數(shù)量增加時(shí),GF檢驗(yàn)會(huì)有比較嚴(yán)重的第一類錯(cuò)誤。我們的研究還表明：有關(guān)兩級(jí)套設(shè)計(jì)模型中隨機(jī)套效應(yīng)的方差分量是否為零的檢驗(yàn),該方法同樣適用。 2.對(duì)異方差下兩級(jí)套設(shè)計(jì)模型的隨機(jī)套效應(yīng)方差分量是否小于等于某個(gè)給定的正數(shù)進(jìn)行檢驗(yàn)。利用重抽樣的思想,提出了一種PB檢驗(yàn)方法,并將其與己存在的GF檢驗(yàn)進(jìn)行比較,用MC方法模擬兩個(gè)檢驗(yàn)方法犯第一類錯(cuò)誤的概率。研究表明：此時(shí)PB檢驗(yàn)有比較好的檢驗(yàn)效果。本文還對(duì)一般混合效應(yīng)模型中的設(shè)計(jì)矩陣進(jìn)行譜分解,在此基礎(chǔ)上,給出一種PB檢驗(yàn)方法,并利用MC方法模擬其犯第一類錯(cuò)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(xué)位授予單位】：北方工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：O212.1

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相關(guān)期刊論文 前1條

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本文編號(hào)：1568632