半参数混合泊松回归模型的估计
发布时间：2018-11-05 17:26
【摘要】：带有重复测量的计数数据经常出现在生物医药、工业、农业等领域中,为了刻画该类数据,泊松随机效应模型得到了很多研究者的重视。然而,在实际问题中,计数数据可能来自于不同总体,同时,它们还会与时间有着某种未知的联系。此时,经典的泊松随机效应模型可能不再适合。为此,本文将利用半参数混合泊松模型对其进行刻画。首先,论文建立了半参数两成分混合泊松模型,其中,每个成分里均引入了非参数函数。本文基于P-样条对未知函数进行了近似,并结合惩罚对数似然函数和EM算法研究了模型的参数估计。其次,为了合理刻画重复测量的计数数据,论文在上述模型的基础上引入了二维随机效应,得到了半参数两成分混合泊松随机效应模型。此模型不仅可以刻画个体内部的相关性,也可以描述不同成分间的相关性。同样,这里也基于P-样条给出惩罚对数似然函数,并在MCEM算法框架下探讨了模型的参数估计。在一定条件下,我们还研究了估计量的相合性和渐近正态性问题,最后,论文利用随机模拟的方法研究了有限样本下两个模型参数估计方法的有效性。同时,我们分别运用半参数一成分泊松随机效应模型和半参数两成分混合泊松随机效应模型对一组实际数据进行拟合,并基于AIC这一常用的准则进行模型选择,可以发现论文所给的模型明显优于单一成分的半参数模型。
[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.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224
本文编号：2312777
[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.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224
【参考文献】
相关期刊论文 前1条
1 解锋昌;韦博成;林金官;;ZI数据的统计分析综述[J];应用概率统计;2009年06期
，本文编号：2312777
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