本文選題：Bayes經(jīng)驗似然　切入點：Bayes局部影響分析　出處：《云南大學》2016年博士論文　論文類型：學位論文

【摘要】：估計方程推斷方法是一種應(yīng)用廣泛的估計方法,許多參數(shù)估計方法,如著名的極大似然法、最小二乘法以及矩估計都是它的特殊情形。估計方程最大的優(yōu)點是不依賴于任何分布,在錯誤指定模型的情形下也可以得到可信賴的結(jié)果,具有穩(wěn)健性。處理估計方程問題的常用方法有廣義矩方法、經(jīng)驗似然方法等,其中基于經(jīng)驗似然方法的估計方程推斷問題引起了很多研究者的興趣。近年來,越來越多的研究者也開始在Bayes框架下考慮經(jīng)驗似然方法的估計方程推斷問題,即Bayes經(jīng)驗似然方法(BEL)。Bayes經(jīng)驗似然方法不僅繼承了傳統(tǒng)經(jīng)驗似然方法和估計方程方法的優(yōu)點,而且便于將可能的多層結(jié)構(gòu)和參數(shù)的附加信息結(jié)合起來。本文對在估計方程下所建立的Bayes經(jīng)驗似然的統(tǒng)計推斷問題及結(jié)構(gòu)方程模型(SEM)的統(tǒng)計推斷問題分別進行了研究。我們考慮了帶有不可忽略缺失數(shù)據(jù)的估計方程的Bayes局部影響分析問題、基于估計方程及經(jīng)驗似然的Bayes變量選擇問題、分位數(shù)結(jié)構(gòu)方程模型(QSEM)在估計方程下的Bayes估計等一系列問題,并研究了結(jié)構(gòu)方程模型的潛在變量選擇問題。首先,對于帶有不可忽略缺失的數(shù)據(jù),我們在參數(shù)先驗信息和缺失機制模型假設(shè)下提出BEL方法來估計未知參數(shù)。同時,建立Bayes局部影響分析方法來對數(shù)據(jù)、先驗分布、估計方程和缺失機制模型等進行敏感性分析。我們提出對數(shù)據(jù)、先驗分布、估計方程和缺失機制模型的單一的或同時的擾動模型,構(gòu)造Bayes擾動流形來反映擾動模型的結(jié)構(gòu)和擾動程度,并在不同的目標函數(shù)下利用一階和二階調(diào)整Bayes局部影響測度來度量各種擾動的影響。此外我們構(gòu)造擬合優(yōu)度統(tǒng)計量來檢驗估計方程假設(shè)的正確性。其次,我們考慮了Bayes經(jīng)驗似然變量選擇問題,利用估計方程建立經(jīng)驗似然函數(shù)并利用收縮Laplace先驗同時實現(xiàn)變量選擇和參數(shù)估計。在一定的正則條件下,我們證明得參數(shù)的后驗概率依概率集中在真實參數(shù)的一領(lǐng)域內(nèi),即參數(shù)后驗概率具有相合性。再次,根據(jù)實際需要,我們建立了分位數(shù)結(jié)構(gòu)方程模型,并采用Bayes經(jīng)驗似然方法對參數(shù)作出估計。其中我們將潛在變量視為缺失數(shù)據(jù)來處理,利用經(jīng)驗似然函數(shù)構(gòu)造潛在變量的條件分布估計,采用線性插值法抽樣插補潛在變量及通過Gibbs抽樣方法獲得參數(shù)的Bayes估計。最后,我們針對結(jié)構(gòu)方程模型的潛在變量選擇問題進行相應(yīng)的研究,提出新的探索性結(jié)構(gòu)方程模型,采用懲罰極大似然方法來識別潛在變量模型的結(jié)構(gòu),并在適當?shù)膽土P函數(shù)和調(diào)節(jié)參數(shù)下,得出估計的相合性和Oracle性質(zhì)。其中我們將潛在變量視為缺失數(shù)據(jù)來處理,采用ECM算法來獲得懲罰極大似然估計。我們采用MM算法來實現(xiàn)ECM算法中的M步,采用IC_Q準則來選擇調(diào)節(jié)參數(shù),并且建立了標準誤差估計。
[Abstract]:Estimation equation inference method is a widely used estimation method, many parameter estimation methods, such as the famous maximum likelihood method, The least square method and moment estimation are its special cases. The greatest advantage of the estimation equation is that it does not depend on any distribution, and can obtain reliable results in the case of misspecifying the model. General moment method, empirical likelihood method and so on, among which the estimation equation inference based on empirical likelihood method has attracted the interest of many researchers in recent years. More and more researchers have begun to consider the estimation equation inference problem of empirical likelihood method under the framework of Bayes. That is, Bayes empirical likelihood method not only inherits the advantages of traditional empirical likelihood method and estimation equation method. Moreover, it is convenient to combine the possible multilayer structure with additional information of parameters. In this paper, the statistical inference problem of Bayes empirical likelihood and the statistical inference problem of structural equation model are discussed respectively. In this paper, we consider the problem of Bayes local impact analysis for the estimation equation with nonnegligible missing data. Based on the estimation equation and empirical likelihood Bayes variable selection problem, the Bayes estimation of the quartile structure equation model under the estimation equation, and so on, the potential variable selection problem of the structural equation model is studied. For data with non-negligible missing data, we propose BEL method to estimate unknown parameters under the assumption of parameter prior information and missing mechanism model. At the same time, we establish a Bayes local impact analysis method to analyze the data and the prior distribution. We propose a single or simultaneous perturbation model for data, prior distribution, estimation equation and missing mechanism model. The Bayes perturbation manifold is constructed to reflect the structure and degree of perturbation of the perturbation model. Under different objective functions, the first and second order Bayes local influence measures are used to measure the effects of various disturbances. In addition, we construct a goodness of fit statistic to test the correctness of the assumptions of the estimation equation. In this paper, we consider the problem of Bayes empirical likelihood variable selection, establish the empirical likelihood function by using the estimation equation and realize the variable selection and parameter estimation simultaneously by using the contraction Laplace priori. We prove that the posteriori probability of parameters is concentrated in a field of real parameters according to probability, that is, the posterior probability of parameters is consistent. Thirdly, according to the actual needs, we establish a quantile structural equation model. The Bayes empirical likelihood method is used to estimate the parameters, in which the potential variables are treated as missing data, and the conditional distribution estimation of the potential variables is constructed by using the empirical likelihood function. The linear interpolation method is used to sample the interpolation potential variables and the Bayes estimation of the parameters is obtained by Gibbs sampling. Finally, we study the potential variable selection problem of the structural equation model and propose a new exploratory structural equation model. The structure of the potential variable model is identified by using the penalty maximum likelihood method, and the consistency and Oracle properties of the estimation are obtained under the appropriate penalty function and adjusting parameters, in which the potential variables are treated as missing data. The ECM algorithm is used to obtain the penalty maximum likelihood estimation, the MM algorithm is used to realize the M-step in the ECM algorithm, the IC_Q criterion is used to select the adjusting parameters, and the standard error estimation is established.
【學位授予單位】：云南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O212.1

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