论文标题:GEE方法在可信度模型结构参数估计中的应用
The Application of GEE Methods in Structure Parameters Estimation of Credibility Models
论文作者
论文导师 朱仲义,论文学位 硕士,论文专业 概率论与数理统计
论文单位 华东师范大学,点击次数 37,论文页数 41页File Size1360K
2006-05-01论文网 http://www.lw23.com/lunwen_148636287/
Credibility theory; Credibility model;structure parameters; Mixed linear model;Pseudolikelihood Method ;QLS Method;GEE2 Method
本文首先概括地讲述了可信度理论在保险实际中的发展史，接下来就几种基本可信度模型的具体表达式、结构参数的一般矩估计以及应用实例，逐一进行了概括性介绍。然而在保险实际中，依照可信度理论恰当地选择可信度模型后，为根据可信度模型最终求得可信度保费的估计值，首先需要研究可信度保费中结构参数的估计。目前，对于可信度模型结构参数的估计，已经提出矩方法、极大似然方法、限制性极大似然方法等多种方法。本文主要介绍并比较拟似然、拟最小二乘等广义估计方程方法在可信度模型结构参数估计中的应用，并且为了更好地应用广义估计方程方法，在探讨估计方法之前，本文首先给出了基本可信度模型的混合线性模型表示形式(Frees，et al．1999)，并以带有独立相关结构的平衡Bǖhlmann模型、Bǖhlmann-Straub模型和带有MA(1)误差结构的平衡Bǖhlmann模型、Bǖhlmann-Straub模型为例，给定结构参数产生计算机模拟数据，然后逐一采用拟似然、拟最小二乘两种广义估计方程方法以及Chi Ho Lo et al．(2006)提出的二阶广义估计方程(GEE2)方法来估计结构参数，最后依照计算机模拟结果验证比较这几种广义估计方程方法的有效性。
In this paper, the development history of credibility theory was described in brief. And then it intruduced the expression and moment estimation of structure parameters and application examples of some basic credibility models in summary.However, in order to obtain the estimate of credibility premium in insurance practise, the estimation of the structure parameters have to been discussed.At present, for the estimation of structure parameters in credibility models, there have been moment-method, MLE-method, REML-method and so on. Here, the paper studied the application of methods of generalized estimating equations (GEEs) in structure parameters estimation of credibility models. Firstly, the paper introduced some basic credibility models in the form of mixed linear models (Frees, et al. 1999). Secondly, The algorithms of Quasi-Least Squares (QLS) Method, Pseudolikelihood Method and GEE2 Method were studied in the paper. These methods were applied to the balanced Buhlmann model and Buhlmann-Straub model with independent error structure and the first-order moving average structure. Finally, the paper verified the validity of these generalized estimation equation methods by simulations.
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