【摘要】：帶有重復(fù)測量的計數(shù)數(shù)據(jù)經(jīng)常出現(xiàn)在生物醫(yī)藥、工業(yè)、農(nóng)業(yè)等領(lǐng)域中,為了刻畫該類數(shù)據(jù),泊松隨機效應(yīng)模型得到了很多研究者的重視。然而,在實際問題中,計數(shù)數(shù)據(jù)可能來自于不同總體,同時,它們還會與時間有著某種未知的聯(lián)系。此時,經(jīng)典的泊松隨機效應(yīng)模型可能不再適合。為此,本文將利用半?yún)?shù)混合泊松模型對其進行刻畫。首先,論文建立了半?yún)?shù)兩成分混合泊松模型,其中,每個成分里均引入了非參數(shù)函數(shù)。本文基于P-樣條對未知函數(shù)進行了近似,并結(jié)合懲罰對數(shù)似然函數(shù)和EM算法研究了模型的參數(shù)估計。其次,為了合理刻畫重復(fù)測量的計數(shù)數(shù)據(jù),論文在上述模型的基礎(chǔ)上引入了二維隨機效應(yīng),得到了半?yún)?shù)兩成分混合泊松隨機效應(yīng)模型。此模型不僅可以刻畫個體內(nèi)部的相關(guān)性,也可以描述不同成分間的相關(guān)性。同樣,這里也基于P-樣條給出懲罰對數(shù)似然函數(shù),并在MCEM算法框架下探討了模型的參數(shù)估計。在一定條件下,我們還研究了估計量的相合性和漸近正態(tài)性問題,最后,論文利用隨機模擬的方法研究了有限樣本下兩個模型參數(shù)估計方法的有效性。同時,我們分別運用半?yún)?shù)一成分泊松隨機效應(yīng)模型和半?yún)?shù)兩成分混合泊松隨機效應(yīng)模型對一組實際數(shù)據(jù)進行擬合,并基于AIC這一常用的準(zhǔn)則進行模型選擇,可以發(fā)現(xiàn)論文所給的模型明顯優(yōu)于單一成分的半?yún)?shù)模型。
[Abstract]:Counting data with repeated measurements are often found in biomedical, industrial, agricultural and other fields. In order to depict such data, Poisson stochastic effect model has been paid attention to by many researchers. In the real world, however, counting data may come from different populations, and they may have some unknown relationship with time. At this point, the classical Poisson stochastic effect model may not be suitable. In this paper, the semi-parametric hybrid Poisson model is used to characterize it. Firstly, a semi-parametric two-component mixed Poisson model is established, in which nonparametric functions are introduced into each component. In this paper, the unknown function is approximated based on the P- spline, and the parameter estimation of the model is studied by combining the penalty logarithmic likelihood function and the EM algorithm. Secondly, in order to describe the counting data of repeated measurements reasonably, the two-dimensional random effect is introduced on the basis of the above model, and the semi-parametric two-component mixed Poisson random effect model is obtained. This model can not only describe the correlation within the individual, but also describe the correlation between different components. Similarly, the penalty logarithmic likelihood function is given based on the P- spline, and the parameter estimation of the model is discussed under the framework of MCEM algorithm. Under certain conditions, we also study the consistency and asymptotic normality of estimators. Finally, we use stochastic simulation to study the validity of two estimation methods for model parameters under finite samples. At the same time, we use semi-parametric Poisson stochastic effect model and semi-parametric two-component mixed Poisson stochastic effect model to fit a set of actual data, and choose the model based on AIC, which is a common criterion. It can be found that the model given in this paper is obviously superior to the semi-parametric model with a single component.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224

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本文編號：2312777