本文關(guān)鍵詞： 縱向數(shù)據(jù) 半?yún)?shù)模型 工具變量 B-樣條 二次推斷函數(shù)估計(jì)　出處：《重慶工商大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著社會的發(fā)展以及統(tǒng)計(jì)學(xué)在各個(gè)領(lǐng)域中的應(yīng)用,分析的實(shí)際問題變得越來越復(fù)雜,在建立統(tǒng)計(jì)模型時(shí),線性回歸模型已不再滿足實(shí)際需求。統(tǒng)計(jì)模型已經(jīng)由線性回歸模型發(fā)展到半?yún)?shù)回歸模型。半?yún)?shù)回歸模型既含參數(shù)分量又含非參數(shù)分量,能夠更好的尋找數(shù)據(jù)的內(nèi)在規(guī)律。當(dāng)解釋變量是外生變量時(shí),大量文獻(xiàn)已討論了半?yún)?shù)回歸模型的統(tǒng)計(jì)方法和理論,也將該模型推廣到了縱向數(shù)據(jù)的情形。但是當(dāng)解釋變量是內(nèi)生變量時(shí),已有的統(tǒng)計(jì)方法和理論不再適用。如何解決縱向數(shù)據(jù)下半?yún)?shù)回歸模型中內(nèi)生解釋變量的問題和組內(nèi)相關(guān)問題是本文的核心。本文考慮縱向數(shù)據(jù)下半?yún)?shù)工具變量模型中興趣參數(shù)的估計(jì),提出了三步估計(jì)過程。首先,利用B-樣條方法逼近半?yún)?shù)模型中的非參數(shù)分量,將半?yún)?shù)回歸模型轉(zhuǎn)化為參數(shù)模型。其次,為了處理內(nèi)生變量,通過引入工具變量,將內(nèi)生變量分解,利用外生變量部分對模型進(jìn)行估計(jì)。然后,先假定參數(shù)已知,估計(jì)非參數(shù)分量。最后,為了得到參數(shù)分量有效的估計(jì),利用二次推斷函數(shù)方法構(gòu)造興趣參數(shù)的目標(biāo)函數(shù)。在一些正則條件下,證明了所得估計(jì)的相合性與漸近正態(tài)性。為了討論所得估計(jì)的有限樣本性質(zhì),對本文提出的方法進(jìn)行了模擬研究。模擬研究表明所提出的估計(jì)方法有效地消除了內(nèi)生變量的影響,而且無論工作相關(guān)矩陣是否正確指定,所得估計(jì)的效率都被提高。最后將所提出的估計(jì)方法應(yīng)用于探究貿(mào)易開放與經(jīng)濟(jì)增長的關(guān)系中,選取國外市場接近度作為工具變量。結(jié)果表明實(shí)際產(chǎn)出與對外貿(mào)易開放度存在顯著正相關(guān)關(guān)系,時(shí)間對實(shí)際產(chǎn)出的影響存在非線性關(guān)系。
[Abstract]:With the development of society and the application of statistics in various fields, the practical problems of analysis become more and more complicated. The statistical model has been developed from the linear regression model to the semi-parametric regression model. The semi-parametric regression model contains both parametric and non-parametric components. When explaining that variables are exogenous variables, a large number of literatures have discussed the statistical method and theory of semi-parametric regression model. The model is also extended to the case of longitudinal data, but when it is explained that the variable is an endogenous variable, The existing statistical methods and theories are no longer applicable. The core of this paper is how to solve the problem of endogenous explanatory variables and intra-group correlation in the semi-parametric regression model of longitudinal data. Estimation of parameters of interest in quantitative models, In this paper, a three-step estimation process is proposed. Firstly, the nonparametric components of the semi-parametric model are approximated by the B-spline method, and the semi-parametric regression model is transformed into a parametric model. Secondly, in order to deal with the endogenous variables, the tool variables are introduced. The endogenous variables are decomposed, and the model is estimated by the exogenous variables. Then, the parameter is known and the nonparametric component is estimated. Finally, in order to obtain the effective estimation of the parameter component, The objective functions of parameters of interest are constructed by using the quadratic inference function method. Under some regular conditions, the consistency and asymptotic normality of the obtained estimates are proved. The simulation results show that the proposed estimation method can effectively eliminate the influence of endogenous variables, regardless of whether the working correlation matrix is correctly assigned. The efficiency of the resulting estimates has been improved. Finally, the proposed estimation method is applied to explore the relationship between trade openness and economic growth. The results show that there is a significant positive correlation between actual output and foreign trade openness, and there is a nonlinear relationship between time and actual output.
【學(xué)位授予單位】：重慶工商大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O212.1;F752;F124.1

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