【作者】 赵金良；

【导师】 宋立新；

【作者基本信息】 大连理工大学 ， 应用数学， 2006， 硕士

【摘要】 本文以最小二乘理论思想为指导,以金融保险中的数据处理问题为背景,研究了具有MA(q)误差线性模型的协方差阵参数的估计问题,提出了分步估计方法,并结合Bootstrap理论、信度理论给出了参数估计的Bootstrap算法。主要的工作如下: 第一章介绍线性模型中最小二乘法的发展,同时经验估费中的信度理论和本文的主要工作。 第二章介绍本文所涉及的一些基本理论知识。第一节重点介绍最小二乘理论;第二节讲述了Bootstrap理论的基本思想并通过具体的例子说明了实现Bootstrap方法的过程。后两节分别介绍了信度理论和MA(q)矩阵的相关知识。 第三章介绍具有MA(q)误差线性模型的协方差阵参数的最小二乘估计。首先引出所假定的模型,然后根据模型的假设及特点构造出方便应用最小二乘法的线性模型。最后列出参数的广义最小二乘估计的表达式,并且说明了表达式中权矩阵的选择方法。 第四章在第三章的基础上,进一步发展了上述最小二乘法在所假设模型中的应用,提出分步估计法。根据模型的特点,我们对待估参数进行分离,并且经过分离后两部分参数均可以用同样的方法构造线性模型,进行最小二乘估计。通过参数分离有效减少了在估计过程中由于参数向量的维数过高所带来的不利影响。 第五章结合Bootstrap理论及最小平方信度理论提出参数估计的Bootstrap算法。并且针对具体问题模拟计算了参数的估计值。在数据稀少的情况下,任何估计的精度往往不够理想。而Bootstrap算法在一定程度上能够克服数据稀少的缺点,对估计的精度有一定的改善。更多还原

【Abstract】 In this dissertation, under the guidance of the least square estimate theory, least squares estimators for covariance parameters for credibility regression models with moving average errors are discussed and some methods for estimating the parameters are presented and improved.The main work is as follows:Chapter 1 of this dissertation is devoted to reviewing the history and development of the least square estimate theory and the credibility theory in insurance.Chapter 2 concerns the backgaound knowlage of this paper. First, the basic theory of the least square estimate method is discussed. Second ,some example are chosen to illustrate how to use the Bootstrap principle.At last,the credibility and MA(q) matrix are introduced.The most important thing in chapter 3 is to discuss how to obtain the least squares estimators for covariance parameters for credibility regression models with MA(q) errors.Based on the prime model,we construct a linear model .So we can obtain the generalized least squares estimators easily.Also, some methods are given to show how to choose weight matrix in the formula of the generalized least squares estimators .Based on the chapter 3,in chapter 4,the least square estimate is developed and the two steps method is presented.With the character of the the prime model,we find the parameter vector can be divided into two parts. Each of them can construct the linear model with the same method in chapter 3.The two steps method can reduce the dimention of the parameter vector.In chapter 5,the Bootstrap method is used to estimate parameters.The Bootstrap method overcome the lack of data.Numerical example is also include in this chapter.更多还原