本文選題：半?yún)?shù)廣義線性混合效應(yīng)模型　切入點：縱向數(shù)據(jù)　出處：《浙江財經(jīng)大學(xué)》2017年碩士論文

【摘要】：縱向數(shù)據(jù)指的是對每個受試單位在不同時間點上重復(fù)測量而收集到的數(shù)據(jù),該數(shù)據(jù)內(nèi)部往往存在相依性。當(dāng)對縱向數(shù)據(jù)進行建模時,必須將組內(nèi)相依性考慮在內(nèi),否則會降低推斷的效。因此,在分析縱向數(shù)據(jù)時,包含有隨機效應(yīng)的混合效應(yīng)模型是常用的模型之一。雖然混合效應(yīng)模型可以用來分析縱向數(shù)據(jù),且具有很強的解釋能力,但過度地假設(shè)響應(yīng)變量和協(xié)變量之間的線性關(guān)系,容易導(dǎo)致興趣參數(shù)不相合的估計。因此,在混合效應(yīng)模型中加入半?yún)?shù)分量,從而形成半?yún)?shù)混合效應(yīng)模型(Partial Linear Mixed Effects Model,簡稱PLMM)。PLMM中既包含固定效應(yīng)和隨機效應(yīng),又包含參數(shù)部分和非參數(shù)部分,充分利用了數(shù)據(jù)的信息,具有良好的適用性和靈活性。因此,該模型被廣泛應(yīng)用于縱向數(shù)據(jù)的分析中,對基于縱向數(shù)據(jù)的PLMM的統(tǒng)計推斷的研究具有一定的理論意義和實用價值。具體地,論文主要包括如下幾個部分:第一章首先簡單介紹了縱向數(shù)據(jù)的背景以及研究意義,然后論述了模型的背景及估計方法,最后介紹了經(jīng)驗似然方法的發(fā)展?fàn)顩r及推斷過程;第二章論述了半?yún)?shù)混合效應(yīng)模型的參數(shù)估計問題,利用廣義經(jīng)驗似然(Generalized Empirical Likelihood,簡稱GEL)方法對該模型進行了參數(shù)估計,得到了參數(shù)分量、非參數(shù)分量以及方差分量的估計量,并在一定條件下證明了估計量的大樣本性質(zhì)。第三章討論了半?yún)?shù)廣義線性混合效應(yīng)模型(Generalized Partial Linear Mixed Effects Model,簡稱GPLMM)參數(shù)估計問題,利用GEL方法對該模型進行了參數(shù)估計,得到了參數(shù)分量、非參數(shù)分量以及方差分量的估計量,并在一定條件下證明了估計量的大樣本性質(zhì)。第四章進行了實證分析,將上述研究方法應(yīng)用到小孩呼吸道感染的醫(yī)學(xué)實例中去,用于說明所提出的方法的有效性。第五章對本文的研究成果、在研究過程中的體會以及值得繼續(xù)研究的地方做了總結(jié)。本文的創(chuàng)新之處主要有以下兩個方面:(1)首次利用GEL方法對GPLMM的統(tǒng)計推斷問題進行研究,使得該方法的應(yīng)用范圍得到了擴展。(2)鑒于縱向數(shù)據(jù)具有組內(nèi)相依性的特點,在構(gòu)造參數(shù)的統(tǒng)計量時,加入了組內(nèi)協(xié)方差陣,從而得到參數(shù)的廣義經(jīng)驗對數(shù)似然比函數(shù)。由于將數(shù)據(jù)的組內(nèi)相依性考慮在內(nèi),模型統(tǒng)計推斷的有效性得到了改善。
[Abstract]:Longitudinal data refers to data collected from repeated measurements at different points in time for each of the subjects, which often have internal dependencies. When modeling longitudinal data, it is important to take intra-group dependencies into account. Otherwise, the effect of inference will be reduced. Therefore, when analyzing longitudinal data, a mixed effect model with random effects is one of the commonly used models. Although the mixed effect model can be used to analyze longitudinal data, it has a strong explanatory power. However, the linear relationship between response variables and covariables is assumed excessively, which easily leads to the estimation of inconsistent parameters of interest. Therefore, a semi-parametric component is added to the mixed effect model. Thus, the partial Linear Mixed Effects Model (PLMM).PLMM), which contains both fixed and random effects, parametric and non-parametric effects, makes full use of the information of the data and has good applicability and flexibility. The model is widely used in the analysis of longitudinal data. The research on statistical inference of PLMM based on longitudinal data has certain theoretical significance and practical value. The thesis mainly includes the following parts: the first chapter briefly introduces the background of longitudinal data and its research significance, then discusses the background and estimation methods of the model, and finally introduces the development and inference process of empirical likelihood method; In the second chapter, the parameter estimation problem of semi-parametric mixed effect model is discussed. The generalized empirical likelihood generalized Empirical Likelihood (Gel) method is used to estimate the parameters of the model, and the estimators of parametric component, nonparametric component and variance component are obtained. In chapter 3, the generalized Partial Linear Mixed Effects model (GPLMMMM) parameter estimation problem is discussed, and the GEL method is used to estimate the parameters of the model. The estimators of parametric component, nonparametric component and variance component are obtained, and the properties of large sample of estimator are proved under certain conditions. The above research method is applied to the medical example of respiratory tract infection in children to illustrate the effectiveness of the proposed method. The main innovations of this paper are the following two aspects: 1) the GEL method is used to study the statistical inference of GPLMM for the first time. In view of the dependence of the longitudinal data within the group, the covariance matrix within the group is added in the construction of the statistics of the parameters. The generalized empirical logarithmic likelihood ratio function of parameters is obtained, and the validity of statistical inference of the model is improved by taking into account the intra-group dependence of the data.
【學(xué)位授予單位】：浙江財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

【參考文獻】

相關(guān)期刊論文 前1條

1 朱仲義;冉昊;;半?yún)?shù)隨機效應(yīng)模型的異方差檢驗[J];數(shù)學(xué)物理學(xué)報;2006年03期

相關(guān)博士學(xué)位論文 前2條

1 李萬斌;縱向數(shù)據(jù)下變系數(shù)混合效應(yīng)模型的有效推斷[D];北京工業(yè)大學(xué);2014年

2 秦國友;半?yún)?shù)混合效應(yīng)模型的穩(wěn)健估計[D];華東師范大學(xué);2007年

相關(guān)碩士學(xué)位論文 前1條

1 張浩;廣義半?yún)?shù)模型的參數(shù)估計與影響分析[D];華東師范大學(xué);2007年

，

本文編號：1666004