本文選題：計數(shù)數(shù)據(jù)　切入點：零膨脹　出處：《貴州民族大學》2017年碩士論文

【摘要】：計數(shù)數(shù)據(jù)是一類重要的數(shù)據(jù)類型,廣泛存在于醫(yī)學、生物和農(nóng)業(yè)等領域中。當計數(shù)數(shù)據(jù)中出現(xiàn)零的比例超出泊松回歸模型或負二項回歸模型等常用計數(shù)模型的預測能力,即數(shù)據(jù)存在零膨脹現(xiàn)象時,若再用經(jīng)典的計數(shù)模型如泊松回歸模型對數(shù)據(jù)進行擬合分析就可能得到錯誤的統(tǒng)計推斷結(jié)論。因此,對計數(shù)數(shù)據(jù)是否存在零膨脹現(xiàn)象的檢驗問題以及對存在零膨脹現(xiàn)象數(shù)據(jù)的模型選擇問題研究具有重要的意義。本文基于Monte Carlo模擬方法就這兩個問題進行了探討分析,具體內(nèi)容如下。第一章,就問題的研究背景、國內(nèi)外研究現(xiàn)狀以及本文的研究思路與研究內(nèi)容安排做了簡單的介紹。第二章,就本文研究所涉及的泊松回歸模型、負二項回歸模型、零膨脹泊松回歸模型和零膨脹負二項回歸模型及相關知識做了簡單的介紹。第三章,針對計數(shù)數(shù)據(jù)是否存在零膨脹現(xiàn)象的檢驗問題,通過Monte Carlo模擬分析方法,探討了不同零膨脹程度、不同均值和不同樣本量條件下,零膨脹泊松回歸模型中七種檢驗方法在檢驗功效和犯第一類錯誤的概率意義下的優(yōu)良性,并結(jié)合實例就七種檢驗方法進行了簡單的說明。第四章,通過Monte Carlo模擬,產(chǎn)生來自零膨脹泊松分布和零膨脹負二項分布的隨機數(shù),并用泊松回歸模型、負二項回歸模型、零膨脹泊松回歸模型和零膨脹負二項回歸模型對產(chǎn)生的隨機數(shù)進行擬合分析,在不同準則下,對模型的優(yōu)良性進行研究。第五章,對本文的研究結(jié)果進行了總結(jié),并結(jié)合本文研究存在的不足,給出了后續(xù)研究的一點思考。
[Abstract]:Counting data is a kind of important data type, which widely exists in the fields of medicine, biology and agriculture. When the proportion of zero in counting data exceeds the prediction ability of common counting models such as Poisson regression model or negative binomial regression model, That is, if the classical counting model such as Poisson regression model is used to fit and analyze the data when there is zero expansion, the wrong statistical inference can be obtained. It is of great significance to examine whether there is zero expansion in the counting data and to study the model selection of the zero expansion data. This paper discusses and analyzes these two problems based on the Monte Carlo simulation method. The main contents are as follows. The first chapter introduces the background of the research, the current situation of the research at home and abroad, the research ideas and the research contents. Chapter two, the Poisson regression model, which is involved in this paper, is introduced. The negative binomial regression model, zero expansion Poisson regression model, zero expansion negative binomial regression model and related knowledge are briefly introduced. In chapter 3, the Monte Carlo simulation analysis method is used to test the existence of zero expansion phenomenon in counting data. Under the conditions of different zero expansion degree, different mean value and different sample size, seven test methods in the zero expansion Poisson regression model are discussed in the sense of test efficacy and probability of making the first kind of error. In chapter 4, through Monte Carlo simulation, random numbers from zero expansion Poisson distribution and zero expansion negative binomial distribution are generated, and Poisson regression model and negative binomial regression model are used. The zero expansion Poisson regression model and the zero expansion negative binomial regression model are used to fit and analyze the generated random numbers. Combined with the shortcomings of this study, this paper gives some thoughts on the follow-up research.
【學位授予單位】：貴州民族大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224

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