信度理论及回归信度模型的研究
发布时间：2019-02-17 11:57
【摘要】：现实生活中许多风险集合中的许多个体风险都是非齐次性的,如何对其中每个风险进行定价；当同时拥有先验经验信息和后验样本信息的时候,如何充分利用所有的信息,如何作出最优估计；信度理论就是在解决上述问题中而产生的。信度理论在保险精算中经验费率调整应用广泛。 从信息利用上来说,贝叶斯估计往往具有绝对的优势,因为它充分利用了可以获得的每个数据的完全信息。由此得出的信度估计就是贝叶斯信度。但是贝叶斯信度估计往往需要多次积分,并且积分计算过程太过于复杂而不具有可操作性。同时它往往需要具体的概率分布,但是这些信息可能没办法获得,也许可以作出经验假设,但是这太有主观性了,同时,做出这样的假设的合理性非常值得怀疑。正是由于存在这样的问题。于是Buhlmann (1967)首次提出了使用线性函数逼近待估值,在满足一定假设条件下,大大简化计算量,得出简单的估计式,而这个估计式恰好可以写成信度理论关键方程的形式,从而建立了现代信度理论。 古典信度理论发源于20世纪早期,也被称为有限波动信度理论。它的基本目的是限制后验样本集的随机波动性对估计的影响。根据后验样本集的随机波动性是否满足事先设定的可接受的估计量的波动性,可以分为完全信度和部分信度。古典信度理论在自然科学中也有广泛应用,如抽样理论、重复实验理论等。本文第二章第三节阐述了古典信度理论的基本框架,介绍其基本原理、完全可信条件。深入探讨了部分信度理论的理论缺陷及其原因,其原因是未考虑先验经验的波动性,正是这个原因可能导致进入信度估计陷阱。并提出了简单的修正方法。 现代信度理论主要建立在贝叶斯估计的理论基础之上。主要考虑到总体中各个个体的分布的参数不一定完全相同。假定总体是服从某一类分布,该分布由参数空间确定,如果事先对参数空间有一定的认识。那么在拥有这些信息的条件下,要估计下一个数据,自然地,可以应用贝叶斯估计。由此产生了贝叶斯信度,其实贝叶斯信度估计和贝叶斯估计是没区别的。但是,由于贝叶斯估计计算往往过于复杂,并且需要知道参数空间的先验分布函数和在给定参数的条件下的后验分布函数,于是产生了许多基于贝叶斯信度估计的其他估计模型。这些模型在很特殊的假设条件下,最终估计式都可以信度理论关键方程的形式,并称为现代信度理论。本文第四章系统阐述了贝叶斯信度的过程和原理,给出引例基于两种假设的贝叶斯估计。第四章第二节介绍了Buhlmann信度是通过线性逼近贝叶斯估计,在均方损失函数下得到。Buhlmann信度最终的形式只依赖于三个参数,而不需要通过假设先验分布,条件分布等,其形式简单,结论形象。在此基础之上,给出了时间序列信度模型的一种近似估计方法。第四章第三节介绍了Buhlmann-Straub模型,它是Buhlmann模型的推广,给出了其非参估计的形式。 无论是Biihlmann信度还是Buhlmann-Straub信度都建立在同个个体独立同分布的基础之上。而经济生活中,许多面板数据在时间维度上都呈一定的趋势性,而回归信度模型就起源于数据的时间趋势性,不同于传统的简单样本数据,时间趋势数据在估计过程中不但要体现每个个体的趋势性,同时考虑个体差异。趋势性反应在回归方程中。在以往的Buhlmann信度模型中,用线性组合去逼近贝叶斯估计,而在回归信度模型中,同样是用线性组合去逼近贝叶斯估计,所不同的是,在Biihlmann信度模型中线性组合中往期经验数据对应的回归系数相等,这是因为考虑到个体样本的独立同分布。而在回归信度模型中,个体样本独立但是不同分布,至少均值就不相等,因而往期经验数据对应的回归系数就不能假定相等了。需要用回归模型来反应这种时间上的趋势性。本文第六章阐述回归信度模型的基本原理和方法,并探讨了存在残差自相关情况下的回归信度模型的迭代估计法。最后给出了计算机模拟的算例,结果显示了较好的效果。
[Abstract]:Many of the individual risks in the real life are non-homogeneous, how to price each risk, and how to make full use of all the information when having the prior experience information and the post-test sample information, and how to make the optimal estimation; The reliability theory is produced in solving the above problems. The reliability theory is widely used in the adjustment of the experience rate in actuarial science. In terms of information utilization, Bayesian estimation tends to have an absolute advantage since it makes full use of the complete letter of each of the data that can be obtained Interest. The reliability estimate is a Bayesian belief. However, Bayesian belief estimation often requires multiple points, and the integration calculation process is too complex to operate Sex. At the same time, it often requires a specific probability distribution, but the information may not be available, and perhaps experience assumptions can be made, but it is too subjective, and the rationality of making such a hypothesis is well worth it. Doubt. It's because of such a question. in that first time, Buhlmann (1967) first proposed that the linear function is used to approximate the value to be valued, and the calculation amount is greatly simplified under the condition of satisfying a certain hypothesis, and the simple estimation formula is obtained, and the estimation formula can be written in the form of the key equation of the reliability theory, thereby establishing the modern reliability theory. On the early part of the 20th century, the classical reliability theory is also known as the limited fluctuation letter. The basic purpose of this is to limit the random fluctuation of the post-check sample set to the estimation. The effect of whether the random fluctuation of the set of post-test samples meets the volatility of the pre-set acceptable estimates and can be divided into full reliability and part The classical reliability theory is widely used in the natural science, such as the sampling theory and the repetition experiment. In the third section of the second chapter, the basic framework of the classical reliability theory is described, and the basic principle of the classical reliability theory is introduced. The paper discusses the theoretical defects and the reasons of the partial reliability theory. The reason is that the fluctuation of the prior experience is not taken into account. It is the reason which may lead to the estimation of the reliability. It's a trap. It's a simple fix. A positive method. The modern reliability theory is mainly based on the theory of Bayesian estimation On the basis of the theory, the parameters of the distribution of the individual in the whole are not one. It is exactly the same. It is assumed that the whole is subject to a class of distribution, which is determined by the parameter space and if the parameter space is in advance it must be recognized that, in the presence of such information, the next data is to be estimated, naturally, applicable, Bayesian estimation, which results in a Bayesian belief, in fact, the Bayesian belief estimation and the Bayesian estimation There is no difference. However, because the Bayesian estimation calculation is often too complex, and the prior distribution function of the parameter space and the post-check distribution function under the condition of a given parameter are needed, a lot of Bayesian belief-based estimation is generated. He estimates the model. Under very special assumptions, the final estimate can be in the form of a key equation of the theory of reliability, and is called the present In chapter four of this paper, the process and the principle of the Bayesian belief are described in the forth chapter, and the two hypotheses are given. The Bayesian estimation is presented in the second section of Chapter 4. The reliability of Buhlmann is estimated by linear approximation and Bayesian estimation. The final form of the Buhlmann's reliability depends only on the three parameters, and it is not necessary to adopt a priori distribution, a condition distribution and the like, and the form is simple. On the basis of this, a close-up of the time series reliability model is given. In the third section, we introduce the Buhlmann-Straub model, which is a generalization of the Buhlmann model, and gives the non-reference of the Buhlmann-Straub model. The form of estimation. Both the Bihmann reliability and the Buhlmann-Straub reliability are established in the same individual as the individual. On the basis of the distribution, many of the panel data show a certain tendency in the time dimension, and the regression reliability model is derived from the time trend of the data, which is different from the traditional simple sample data. The time trend data is not only reflected in the estimation process. The trend of an individual. take into account individual differences. In the previous Buhlmann reliability model, a linear combination is used to approximate the Bayesian estimation, and in the regression reliability model, a linear combination is used to approximate the Bayesian estimation. The regression coefficient is equal because the individual sample is taken into account In the regression reliability model, the individual samples are independent but different, at least the mean value is not equal, so the regression coefficient corresponding to the time experience data It's not supposed to be the same. We need to use the regression model to respond to this. In chapter 6 of this paper, the basic principle and method of the regression reliability model are described, and the regression reliability model in the case of residual self-correlation is discussed. The iterative estimation method of the type is given. Finally, the computer simulation calculation example is given, and the result is obvious.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3
本文编号：2425142
[Abstract]:Many of the individual risks in the real life are non-homogeneous, how to price each risk, and how to make full use of all the information when having the prior experience information and the post-test sample information, and how to make the optimal estimation; The reliability theory is produced in solving the above problems. The reliability theory is widely used in the adjustment of the experience rate in actuarial science. In terms of information utilization, Bayesian estimation tends to have an absolute advantage since it makes full use of the complete letter of each of the data that can be obtained Interest. The reliability estimate is a Bayesian belief. However, Bayesian belief estimation often requires multiple points, and the integration calculation process is too complex to operate Sex. At the same time, it often requires a specific probability distribution, but the information may not be available, and perhaps experience assumptions can be made, but it is too subjective, and the rationality of making such a hypothesis is well worth it. Doubt. It's because of such a question. in that first time, Buhlmann (1967) first proposed that the linear function is used to approximate the value to be valued, and the calculation amount is greatly simplified under the condition of satisfying a certain hypothesis, and the simple estimation formula is obtained, and the estimation formula can be written in the form of the key equation of the reliability theory, thereby establishing the modern reliability theory. On the early part of the 20th century, the classical reliability theory is also known as the limited fluctuation letter. The basic purpose of this is to limit the random fluctuation of the post-check sample set to the estimation. The effect of whether the random fluctuation of the set of post-test samples meets the volatility of the pre-set acceptable estimates and can be divided into full reliability and part The classical reliability theory is widely used in the natural science, such as the sampling theory and the repetition experiment. In the third section of the second chapter, the basic framework of the classical reliability theory is described, and the basic principle of the classical reliability theory is introduced. The paper discusses the theoretical defects and the reasons of the partial reliability theory. The reason is that the fluctuation of the prior experience is not taken into account. It is the reason which may lead to the estimation of the reliability. It's a trap. It's a simple fix. A positive method. The modern reliability theory is mainly based on the theory of Bayesian estimation On the basis of the theory, the parameters of the distribution of the individual in the whole are not one. It is exactly the same. It is assumed that the whole is subject to a class of distribution, which is determined by the parameter space and if the parameter space is in advance it must be recognized that, in the presence of such information, the next data is to be estimated, naturally, applicable, Bayesian estimation, which results in a Bayesian belief, in fact, the Bayesian belief estimation and the Bayesian estimation There is no difference. However, because the Bayesian estimation calculation is often too complex, and the prior distribution function of the parameter space and the post-check distribution function under the condition of a given parameter are needed, a lot of Bayesian belief-based estimation is generated. He estimates the model. Under very special assumptions, the final estimate can be in the form of a key equation of the theory of reliability, and is called the present In chapter four of this paper, the process and the principle of the Bayesian belief are described in the forth chapter, and the two hypotheses are given. The Bayesian estimation is presented in the second section of Chapter 4. The reliability of Buhlmann is estimated by linear approximation and Bayesian estimation. The final form of the Buhlmann's reliability depends only on the three parameters, and it is not necessary to adopt a priori distribution, a condition distribution and the like, and the form is simple. On the basis of this, a close-up of the time series reliability model is given. In the third section, we introduce the Buhlmann-Straub model, which is a generalization of the Buhlmann model, and gives the non-reference of the Buhlmann-Straub model. The form of estimation. Both the Bihmann reliability and the Buhlmann-Straub reliability are established in the same individual as the individual. On the basis of the distribution, many of the panel data show a certain tendency in the time dimension, and the regression reliability model is derived from the time trend of the data, which is different from the traditional simple sample data. The time trend data is not only reflected in the estimation process. The trend of an individual. take into account individual differences. In the previous Buhlmann reliability model, a linear combination is used to approximate the Bayesian estimation, and in the regression reliability model, a linear combination is used to approximate the Bayesian estimation. The regression coefficient is equal because the individual sample is taken into account In the regression reliability model, the individual samples are independent but different, at least the mean value is not equal, so the regression coefficient corresponding to the time experience data It's not supposed to be the same. We need to use the regression model to respond to this. In chapter 6 of this paper, the basic principle and method of the regression reliability model are described, and the regression reliability model in the case of residual self-correlation is discussed. The iterative estimation method of the type is given. Finally, the computer simulation calculation example is given, and the result is obvious.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3
【参考文献】
相关期刊论文 前1条
1 唐国强;;具有线性趋势的回归信度模型中的估计和检验[J];应用概率统计;2009年03期
，本文编号：2425142
本文链接：https://www.wllwen.com/jingjilunwen/bxjjlw/2425142.html
