本文選題：部分線(xiàn)性變系數(shù)EV模型 + 調(diào)整加權(quán)最小二乘估計(jì)�。� 參考：《蘭州理工大學(xué)》2017年碩士論文

【摘要】：部分線(xiàn)性變系數(shù)模型是近年來(lái)提出的一個(gè)具有很強(qiáng)實(shí)際應(yīng)用性的模型.該模型形式包含了很多子模型,例如參數(shù)、非參數(shù)以及半?yún)?shù)模型都可以看做為部分線(xiàn)性變系數(shù)模型的特例,所以其不但具有線(xiàn)性模型形式簡(jiǎn)單,易于觀(guān)察的優(yōu)點(diǎn)、非參數(shù)模型穩(wěn)健的特征,還能夠動(dòng)態(tài)的表達(dá)協(xié)變量與相應(yīng)變量之間的相互關(guān)系.通常在建立回歸模型時(shí),我們認(rèn)為所得到的觀(guān)測(cè)數(shù)據(jù)都是完整的,準(zhǔn)確的,且誤差項(xiàng)彼此相互獨(dú)立并不考慮數(shù)據(jù)測(cè)量誤差,或者缺失響應(yīng)變量.但是在實(shí)際生產(chǎn)過(guò)程中,沒(méi)有測(cè)量誤差或者缺失響應(yīng)變量的數(shù)據(jù),通常很難得到,或者需要付出極大成本去提高精度.而在實(shí)際生產(chǎn)過(guò)程中,這都是不現(xiàn)實(shí)的.所以當(dāng)研究回歸模型時(shí)需要考慮到這些外部因素對(duì)模型的影響,然后再對(duì)模型的參數(shù)進(jìn)行估計(jì).第一章,主要介紹了本文所研究問(wèn)題的背景、部分線(xiàn)性變系數(shù)EV模型的研究發(fā)展、現(xiàn)狀以及本文研究所需的一些理論知識(shí).第二章,考慮模型在帶有測(cè)量誤差及約束條件下情形下的回歸情況.運(yùn)用調(diào)整最小二乘估計(jì)和Lagrange乘數(shù)法估計(jì)未知參數(shù)和系數(shù)函數(shù),在一定條件下證明參數(shù)、非參數(shù)函數(shù)估計(jì)的相合性,并模擬實(shí)驗(yàn)結(jié)果.第三章,研究了響應(yīng)變量缺失下,參數(shù)具有線(xiàn)性約束且參數(shù)部分和非參數(shù)部分都帶有測(cè)量誤差的部分線(xiàn)性變系數(shù)模型的估計(jì)問(wèn)題,利用最小二乘法和局部糾偏方法給出模型中參數(shù)和系數(shù)函數(shù)的估計(jì),在一定的條件下證明了它們的漸近性質(zhì).
[Abstract]:Partial linear variable coefficient model is a model with strong practical application proposed in recent years. The model form contains many submodels, such as parametric, nonparametric and semi-parametric models, which can be regarded as special cases of partial linear variable coefficient models, so it not only has the advantages of simple form of linear model, but also easy to observe. The robust features of the nonparametric model can also dynamically express the relationship between the covariable and the corresponding variable. When we build the regression model, we think that the observed data are complete and accurate, and the error terms are independent of each other without considering the measurement error or the missing response variables. However, in the actual production process, the data without measurement errors or missing response variables are usually difficult to obtain, or need to pay a great deal of cost to improve the accuracy. In the actual production process, this is unrealistic. Therefore, when studying the regression model, we should consider the influence of these external factors on the model, and then estimate the parameters of the model. In the first chapter, we introduce the background of the problem, the research development of partial linear variable coefficient EV model, the present situation and some theoretical knowledge needed in this paper. In chapter 2, the regression of the model with measurement error and constraint is considered. By using the method of adjusted least square and Lagrange multiplier to estimate the unknown parameter and coefficient function, the consistency of parameter and nonparametric function estimation is proved under certain conditions, and the experimental results are simulated. In chapter 3, we study the estimation of partial linear variable coefficient model with linear constraints and measurement errors in both parametric and nonparametric parts under the absence of response variables. The estimation of the parameter and coefficient function in the model is given by using the least square method and the local correction method. Their asymptotic properties are proved under certain conditions.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212.1

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