Generalized Linear Model Research And Its Application For Vehicle Insurance

Generalized linear model has the important influence on the regression model in the application of statistics. It has a lot of good properties which the classical linear regression model does not have. Many researchers have studied generalized linear model. Therefore the generalized linear model is widely applied to the specific problems.In this thesis, the main research contents about the generalized linear model include four parts. First, we introduce the basic concepts of the generalized linear model in detail, list several kinds of common generalized linear models and point out the advantages of the generalized linear model through the comparison of generalized linear model and classical regression model. Secondly, we study the two parameter estimation methods of the generalized linear model:maximum likelihood estimation and two-parameter estimation. According to their theoretical formulas, we compare these two methods. And then, we introduce several kinds of hypothesis testing methods which are commonly used in the generalized linear model. Finally, we apply the generalized linear model in the motor vehicle insurance. The parameters in the generalized linear model are estimated by maximum likelihood estimation and two-parameter estimation respectively. According to the Wald statistic, we eliminate two variables which are not significant. And the parameters are estimated again. The two-parameter estimation obtains the better test result than maximum likelihood estimation, which illustrates that the two-parameter estimation overcomes the effect of multi-collinearity to a certain extent. Therefore, we should choose the two-parameter estimation for the estimating the parameters in the generalized linear model.There are two contributions of our thesis. The first contribution is that before building generalized linear model we verify the data distribution type which provides the guidance for choosing reasonable generalized linear model. The second contribution is that according to different degrees of multi-collinearity of explanatory variables, we carry on the contrast experiment by using the monte carlo simulation method. The experimental results show that the two-parameter estimation better than maximum likelihood estimation. Previous works for predicting motor vehicle insurance claim frequency are conducted using maximum likelihood estimation for parameters estimation, but in our thesis we first propose that the two-parameter estimation is applied to this application. And we obtain better results than those produced by the maximum likelihood estimation.