Two Steps Method And Bootstrap Algorithm For Covariance Parameters For Credibility Regression Models With Moving Average Errors

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.