本文選題：線性混合模型 + 固定效應�。� 參考：《青島科技大學》2015年碩士論文

【摘要】：線性混合模型在生物、經(jīng)濟、計算機等領(lǐng)域具有很廣泛的應用,其參數(shù)估計問題是統(tǒng)計學家研究的重點之一。本文針對固定效應與隨機效應兩類參數(shù)的估計方法進行研究,并得出一些新的結(jié)論。對于固定效應的參數(shù)估計,介紹了線性可估函數(shù)c'β的最小二乘估計(LSE)與兩步估計分別為最佳線性無偏估計(BLUE)的條件,并分析了BLUE的可容許性。在此基礎(chǔ)上,將線性混合模型轉(zhuǎn)化為滿足Gauss-Markov段設(shè)的模型,給出在該假設(shè)下LSE為BLUE的充分條件；探討了利用奇異值分解對兩步估計進行改進的方法,并討論了改進后兩步估計具有的一些新性質(zhì)；由于LSE經(jīng)常會有精度上的損失,引進相對效率的概念,以生長曲線模型與權(quán)回歸模型為例,分別定義了兩種模型新的相對效率,并給出它們的上下界。新的相對效率考慮了各分量之間協(xié)方差產(chǎn)生的影響,提高了靈敏度。對于隨機效應的參數(shù)估計,分別介紹了方差分析估計(ANOVAE)與譜分解估計(SDE)方法的相關(guān)性質(zhì)以及具體應用。在一個新的估計類中,改進了ANOVAE方法,探討了改進估計的非負性,同時,基于全空間的多層正交直和分解,將ANOVAE方法推廣到不依賴于隨機效應正態(tài)假設(shè)的線性混合模型中；進一步研究SDE的性質(zhì),將SDE推廣到一般的線性混合模型中,討論了SDE與ANOVAE相等的充要條件,給出三個具體實例進行分析驗證。
[Abstract]:Linear mixed model has been widely used in biology, economy, computer and so on. The parameter estimation problem is one of the key points in the research of statisticians. In this paper, two kinds of parameter estimation methods, fixed effect and random effect, are studied, and some new conclusions are obtained. For the parameter estimation of fixed effect, the condition that the least square estimator (LSE) and the two-step estimator of the linear estimable function c'尾 are respectively the best linear unbiased estimator (blue) are introduced, and the admissibility of blue is analyzed. On this basis, the linear mixed model is transformed into a model satisfying Gauss-Markov segment, and the sufficient conditions for LSE to be blue under this assumption are given, and the method of improving the two-step estimation by using singular value decomposition is discussed. Some new properties of the improved two-step estimation are discussed. As LSE often has a loss of precision, the concept of relative efficiency is introduced. Taking growth curve model and weight regression model as examples, the new relative efficiency of two models is defined respectively. Their upper and lower bounds are given. The new relative efficiency takes into account the influence of covariance between components and improves the sensitivity. For the parameter estimation of random effects, the properties and applications of ANOVAE and SDE are introduced. In a new class of estimators, the ANOVAE method is improved, and the nonnegativity of the improved estimation is discussed. At the same time, the ANOVAE method is extended to the linear mixed model which does not depend on the assumption of random effect normality based on the multilayer orthogonal sum decomposition in the whole space. The properties of SDE are further studied, and the SDE is extended to the general linear mixed model. The sufficient and necessary conditions for the equality of SDE and ANOVAE are discussed, and three examples are given for analysis and verification.
【學位授予單位】：青島科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O212.1

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相關(guān)期刊論文 前1條

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本文編號：2099656