本文關(guān)鍵詞： 擬似然 函數(shù)型變量 廣義半函數(shù)部分線性模型　出處：《云南大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著社會(huì)的發(fā)展,計(jì)算機(jī)存儲(chǔ)能力和處理速度的提升,我們?cè)诃h(huán)境科學(xué)、化學(xué)、生物學(xué)、醫(yī)學(xué)、經(jīng)濟(jì)學(xué)等越來(lái)越多的領(lǐng)域觀測(cè)到的數(shù)據(jù)越來(lái)越精細(xì)。例如,對(duì)一個(gè)現(xiàn)象我們可以觀測(cè)一個(gè)大樣本的變量,進(jìn)一步我們來(lái)看一個(gè)通常的情形：某個(gè)隨機(jī)變量可以在范圍(t min,tmax)的一些時(shí)間點(diǎn)上取值,則它的一個(gè)觀測(cè)樣本可以通過隨機(jī)族{X(tj)} j=1,....,J來(lái)表示。在現(xiàn)代統(tǒng)計(jì)中,給定范圍時(shí)的觀測(cè)數(shù)據(jù)越來(lái)越多意味著連續(xù)不斷的常數(shù)越來(lái)越靠近。傳統(tǒng)統(tǒng)計(jì)方法和統(tǒng)計(jì)模型在處理這類數(shù)據(jù)時(shí)存在很多問題,如過擬合和維數(shù)禍根問題。為解決這些困難,統(tǒng)計(jì)學(xué)者們把這些觀測(cè)到的大樣本數(shù)據(jù)考慮成連續(xù)族,將每個(gè)個(gè)體看成一條曲線,從而對(duì)曲線數(shù)據(jù)進(jìn)行統(tǒng)計(jì)分析。這就是本文中函數(shù)型數(shù)據(jù)的基本思想。部分線性模型理論首先由Engle et al(1986)提出,隨后被廣泛研究和應(yīng)用在應(yīng)用統(tǒng)計(jì)的許多領(lǐng)域。這種模型允許一部分解釋變量為參數(shù)形式,而另一部分解釋變量為非參形式。隨后Thomas把此模型推廣到廣義形式。本文應(yīng)用擬似然方法來(lái)對(duì)廣義部分線性模型進(jìn)行估計(jì),并利用近年來(lái)函數(shù)型數(shù)據(jù)在非參數(shù)統(tǒng)計(jì)方面的發(fā)展,把函數(shù)型數(shù)據(jù)引入到解釋變量的估計(jì)中來(lái),研究廣義半函數(shù)部分線性模型,對(duì)模型中參數(shù)估計(jì)量的一些漸進(jìn)性質(zhì)進(jìn)行了說明。最后,用一個(gè)實(shí)值例子來(lái)說明本文中模型的估計(jì)效果。
[Abstract]:With the development of society and the improvement of computer storage capacity and processing speed, we have observed more and more fine data in more and more fields such as environmental science, chemistry, biology, medicine, economics and so on. For example. For a phenomenon we can look at a large sample of variables, and further, let's look at the usual situation: a random variable can be selected at some point in time in the range of mint / t _ max. (_ _ _). Then one of its observation samples can be represented by the random family {Xtj)} JJ. The increasing number of observed data in a given range means that the constant is getting closer and closer. Traditional statistical methods and statistical models have many problems in dealing with such data. In order to solve these difficulties, statisticians consider these large sample data as a continuous family and treat each individual as a curve. This is the basic idea of the functional data in this paper. The partial linear model theory was first put forward by Engle et alin1986). It has been widely studied and applied in many fields of applied statistics. This model allows some explanatory variables to be parameterized. Then Thomas extended the model to the generalized form. In this paper, the quasi-likelihood method is used to estimate the generalized partial linear model. Based on the development of nonparametric statistics of functional data in recent years, this paper introduces the functional data into the estimation of explanatory variables, and studies the generalized semi-functional partial linear model. Some asymptotic properties of the parameter estimator in the model are explained. Finally, a real value example is used to illustrate the estimation effect of the model in this paper.
【學(xué)位授予單位】：云南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O212.1
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本文編號(hào)：1467274