本文選題：Poisson回歸 + D-最優(yōu)��； 參考：《上海師范大學(xué)》2016年碩士論文

【摘要】：當(dāng)今社會信息高速發(fā)展,大量信息以數(shù)據(jù)的形式存在,信息的多樣性使得數(shù)據(jù)形式也具有多樣性。在處理離散型數(shù)據(jù)時,傳統(tǒng)的線性模型具有很大的局限性,此時就需要借助廣義線性模型。Poisson回歸模型是廣義線性模型的一個重要的分支,主要用來研究計數(shù)型數(shù)據(jù)。近年來,Poisson回歸模型的最優(yōu)設(shè)計問題逐漸引起大家的關(guān)注�，F(xiàn)有的研究中多是基于模型中只含定量因子的情形,對含有定性因子的Poisson回歸模型的研究較少。且多因子設(shè)計問題較為復(fù)雜,單因子設(shè)計問題則更為簡單,其研究也比較成熟。所以本文旨在將復(fù)雜的多因子問題轉(zhuǎn)化為簡單的單因子問題,主要就以下兩方面進行了研究：對含有多個定量因子的Poisson回歸可加模型的D-最優(yōu)設(shè)計問題,首先將回歸函數(shù)作典則變換以消除對參數(shù)的依賴性;然后轉(zhuǎn)化成求異方差線性可加模型的D-最優(yōu)設(shè)計問題,接下來就此問題進行研究；對其異方差子模型,定義了一種新的最優(yōu)準則,通過計算方向?qū)?shù)得到其等價條件并據(jù)此進行算法構(gòu)造；最后對回歸函數(shù)作中心化變換并借助一般等價性定理,證明了其D-最優(yōu)設(shè)計是其異方差子模型與其同方差子模型的最優(yōu)設(shè)計的乘積設(shè)計,從而使問題得到解決。對含有定性因子的多因子Poisson回歸可加模型的D-最優(yōu)設(shè)計問題,則按照慣例首先引入啞變量,然后將回歸函數(shù)作典則變換,并將設(shè)計問題轉(zhuǎn)化為該含定性因子的部分異方差線性可加模型的設(shè)計問題；最后利用第一部分的結(jié)論,解決此異方差模型的設(shè)計問題。兩方面的研究都表明：多因子Poisson回歸模型的設(shè)計問題可以轉(zhuǎn)化為單因子設(shè)計問題來解決,從而使設(shè)計問題得到簡化。此外,本文就這兩類問題都給出了例題進行演示。
[Abstract]:Nowadays, with the rapid development of social information, a great deal of information exists in the form of data. When dealing with discrete data, the traditional linear model has great limitations. In this case, the generalized linear model .Poisson regression model is an important branch of the generalized linear model, which is mainly used to study the counting-type data. In recent years, the optimal design of Poisson regression model has attracted more and more attention. Most of the existing studies are based on the case where there are only quantitative factors in the model, but the Poisson regression model with qualitative factors is less studied. The problem of multi-factor design is more complex, the problem of single-factor design is more simple, and its research is more mature. Therefore, this paper aims to transform the complex multi-factor problem into a simple single-factor problem. This paper mainly studies the following two aspects: the D- optimal design problem for Poisson regression additive model with multiple quantitative factors. Firstly, the regression function is canonical transformed to eliminate the dependence on parameters, and then the D- optimal design problem of the linear additive model of heteroscedasticity is transformed into a D- optimal design problem, and the heteroscedasticity submodel is studied. In this paper, a new optimal criterion is defined, and the equivalent condition is obtained by calculating the directional derivative and the algorithm is constructed. Finally, the central transformation of the regression function is made and the general equivalence theorem is used. It is proved that the D- optimal design is the product design of the optimal design of its heteroscedasticity submodel and its isomorphic submodel, so that the problem can be solved. For the D- optimal design problem of multivariate Poisson regression additive model with qualitative factors, the dummy variable is first introduced according to the convention, and then the regression function is canonical transformed. The design problem is transformed into the design problem of the partial heteroscedasticity linear additive model with qualitative factors, and the design problem of the heteroscedasticity model is solved by using the conclusions in the first part. Both studies show that the design problem of multi-factor Poisson regression model can be transformed into a single-factor design problem and the design problem can be simplified. In addition, examples of both kinds of problems are given in this paper.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：F224

【參考文獻】

相關(guān)碩士學(xué)位論文 前1條

1 張旭;含有定性因子的多項式模型的D-最優(yōu)設(shè)計[D];上海師范大學(xué);2013年

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本文編號：2088938