本文選題：高維數(shù)據(jù) + 對數(shù)線性模型　； 參考：《廣西大學(xué)》2015年碩士論文

【摘要】：1986年Liang和Zeger從廣義線性模型推廣(GLM)而得到廣義估計方程(Generalized estimating equations, GEE), GEE是對縱向數(shù)據(jù)進行回歸分析的一類重要方法,其主要特點是引入了工作相關(guān)(working correlation)矩陣.自推廣以來,廣義估計方程在理論和應(yīng)用得到了很大的發(fā)展.在傳統(tǒng)的回歸模型分析中,一般是假定“樣本量n→∞,而協(xié)變量個數(shù)p固定”的情形.隨著高維數(shù)據(jù)的出現(xiàn),“當(dāng)樣本量n→∞,協(xié)變量個數(shù)pn→∞”這一情形也逐漸受到統(tǒng)計學(xué)家的關(guān)注.本文的主要研究工作是,基于廣義估計方程方法研究協(xié)變量個數(shù)pn趨于無窮的對數(shù)線性Poisson分布模型的漸近性質(zhì).在Pn3/n→0(n→+∞)等正則條件下,證明GEE估計的存在性,相合性和漸近正態(tài)性.推廣Xie和Yang (Ann.Statist.31(2003)310-347), Balan和Schiopu-Kratina (Ann.Statist.33(2005)522-541)的漸近結(jié)果到協(xié)變量是高維情形,也推廣了Wang的結(jié)果(Ann. Statist.39(2011)389-417)到響應(yīng)變量是無界的情況.
[Abstract]:In 1986, Liang and Zeger obtained generalized estimating equations from generalized linear model (GLM). Gee is an important method for regression analysis of longitudinal data. The main characteristic of Liang and Zeger is the introduction of work-related (working correlation) matrix. Since its extension, the generalized estimation equation has been greatly developed in theory and application. In the traditional regression model analysis, it is generally assumed that "sample size n 鈭，

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