Several Estimates And Comparisons Of Generalized Linear Models

As a generalization of the linear model,the generalized linear model is more widely used.It is suitable for the continuous random variables,but also to adapt to the dependent variable for the discrete random variables.This determines its more extensive application value.Generalized linear model can be used in insurance,finance,medicine,social statistics and other fields.Parameter estimation is an important part of Statistics.It is the basis for the study of other statistical properties.At present,the most widely used method of parameter estimation in the generalized linear model is maximum likelihood estimation.It can be obtained by iterative method to estimate the parameter of interest.In the generalized linear model,the maximum likelihood estimator performs well under normal conditions,is a good parameter estimation method.However,the maximum likelihood estimation of parameters in generalized linear models is not the best parameter estimation method in some cases.For example,sometimes the estimated parameters are subject to partial constraints,if these constraints are not considered to estimate the parameters,then the estimated value may be biased comparing with the real value.So in this paper we introduce the shrinkage estimate of generalized linear model,trying to improve this situation.The asymptotic property of shrinkage estimation is discussed,the asymptotic risk function of the shrinkage estimation is given and compared with the asymptotic risk function of the maximum likelihood estimator,and the numerical simulation of shrinkage estimation is also given.In addition,when the generalized linear model has multi-collinearity,the mean square error of the MLE will be very large.At this point,MLE is not a good parameter estimation method.In this paper,we will discuss some methods to overcome the multi-collinearity of the model,and the numerical example is used to compare these methods.In addition,the ridge estimation of generalized linear model is improved,the concept of generalized ridge estimation in generalized linear model is proposed,and some related properties are proved.It is shown that the generalized ridge estimator of the generalized linear model is better than the generalized linear model.