廣義泊松Hurdle回歸模型及其統(tǒng)計(jì)診斷
發(fā)布時(shí)間：2018-08-02 19:14
【摘要】：計(jì)數(shù)數(shù)據(jù)是一種常見的離散型數(shù)據(jù),在我們?nèi)粘Ｉ钪械谋姸囝I(lǐng)域都存在著大量的計(jì)數(shù)數(shù)據(jù).處理計(jì)數(shù)數(shù)據(jù)的一個(gè)最基本的模型是泊松回歸模型,但是他的局限性在于均值必須等于方差,這在實(shí)際中是很難滿足的.而廣義泊松分布是標(biāo)準(zhǔn)泊松分布的自然推廣,它引入了散度參數(shù),能夠用來權(quán)衡均值和方差的關(guān)系.另一方面,有些計(jì)數(shù)數(shù)據(jù)還會(huì)出現(xiàn)大量的零數(shù)據(jù),這些數(shù)據(jù)中的零的個(gè)數(shù)要明顯多于泊松分布、廣義泊松分布產(chǎn)生零的個(gè)數(shù),我們稱這些數(shù)據(jù)為含零過多的數(shù)據(jù).本文主要研究的對(duì)象就是這類含零過多并且期望不等于方差的特殊數(shù)據(jù),詳細(xì)介紹了處理這類數(shù)據(jù)的一種典型模型——廣義泊松Hurdle回歸模型.具體研究內(nèi)容如下.本文第一章介紹了研究的背景.第二章介紹了廣義泊松回歸模型、Hurdle回歸模型和廣義泊松Hurdle回歸模型,并且給出了廣義泊松Hurdle回歸模型的參數(shù)估計(jì)方法.第三章給出了基于數(shù)據(jù)刪除模型的統(tǒng)計(jì)診斷量,給出了參數(shù)估計(jì)的一步近似公式、廣義Cook距離和似然距離,并且對(duì)散度參數(shù)的存在性進(jìn)行檢驗(yàn).第四章給出了模型的選擇方法,通過這些準(zhǔn)則來判斷哪個(gè)模型的擬合效果更好.第五章用Monte Carlo隨機(jī)模擬方法來說明第二章第三章所介紹的統(tǒng)計(jì)量的有效性.第六章通過耳病發(fā)生次數(shù)的例子來說明對(duì)于這種含零過多并且期望不等于方差的數(shù)據(jù)用本文重點(diǎn)介紹的廣義泊松Hurdle回歸模型擬合效果最好.論文最后給出結(jié)論和進(jìn)一步研究的問題.
[Abstract]:Counting data is a kind of common discrete data. There are a lot of counting data in many fields of our daily life. One of the most basic models for dealing with counting data is the Poisson regression model, but its limitation is that the mean value must be equal to the variance, which is difficult to satisfy in practice. The generalized Poisson distribution is a natural generalization of the standard Poisson distribution. It introduces divergence parameters and can be used to weigh the relationship between mean and variance. On the other hand, a large number of zero data will appear in some counting data, the number of zeros in these data is obviously more than that in Poisson distribution, and the generalized Poisson distribution produces the number of zero. The object of this paper is this kind of special data with zero excess and expected variance. A typical model for dealing with this kind of data, generalized Poisson Hurdle regression model, is introduced in detail. The specific contents of the study are as follows. The first chapter introduces the background of the research. In chapter 2, the Hurdle regression model and the generalized Poisson Hurdle regression model are introduced, and the parameter estimation method of the generalized Poisson Hurdle regression model is given. In chapter 3, the statistical diagnostics based on data deletion model are given. The one-step approximation formula, generalized Cook distance and likelihood distance for parameter estimation are given, and the existence of divergence parameters is tested. In chapter 4, the method of model selection is given, which is used to judge which model is better. Chapter 5 uses Monte Carlo stochastic simulation method to illustrate the validity of the statistics introduced in Chapter 2 and Chapter 3. Chapter 6 shows that the generalized Poisson Hurdle regression model is the best fitting method for the data with zero excess and expected variance through an example of the occurrences of ear diseases. Finally, the conclusion and further research are given.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1
本文編號(hào)：2160458
[Abstract]:Counting data is a kind of common discrete data. There are a lot of counting data in many fields of our daily life. One of the most basic models for dealing with counting data is the Poisson regression model, but its limitation is that the mean value must be equal to the variance, which is difficult to satisfy in practice. The generalized Poisson distribution is a natural generalization of the standard Poisson distribution. It introduces divergence parameters and can be used to weigh the relationship between mean and variance. On the other hand, a large number of zero data will appear in some counting data, the number of zeros in these data is obviously more than that in Poisson distribution, and the generalized Poisson distribution produces the number of zero. The object of this paper is this kind of special data with zero excess and expected variance. A typical model for dealing with this kind of data, generalized Poisson Hurdle regression model, is introduced in detail. The specific contents of the study are as follows. The first chapter introduces the background of the research. In chapter 2, the Hurdle regression model and the generalized Poisson Hurdle regression model are introduced, and the parameter estimation method of the generalized Poisson Hurdle regression model is given. In chapter 3, the statistical diagnostics based on data deletion model are given. The one-step approximation formula, generalized Cook distance and likelihood distance for parameter estimation are given, and the existence of divergence parameters is tested. In chapter 4, the method of model selection is given, which is used to judge which model is better. Chapter 5 uses Monte Carlo stochastic simulation method to illustrate the validity of the statistics introduced in Chapter 2 and Chapter 3. Chapter 6 shows that the generalized Poisson Hurdle regression model is the best fitting method for the data with zero excess and expected variance through an example of the occurrences of ear diseases. Finally, the conclusion and further research are given.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1
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，本文編號(hào)：2160458
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