Empirical Likelihood For Poisson Regerssion Models With Dispersion And Missing Data

The question of counting in life is often linked to the Poisson distribution,for example,when the number of occurrences of an event occurs over a given period of time,can be modeled using the Poisson regression model.One of the basic assumptions of the Poisson regression model is that the mean of the population distribution is equal to the variance,but in reality the condition is sometimes not satisfied.This is not equal to the variance of the case known as the distribution of the phenomenon,in which case the establishment of the model need to consider the distribution of the situation.In order to solve this problem,we use the double generalized linear model to model the mean and the divergence simultaneously.Based on the extended quasi-likelihood estimation method in empirical likelihood study,we discuss the parameter estimation of the model in the case of stochastic loss of response variable Methods,including the following:First,a Poisson regression model with spreading problem is introduced,and a divergence parameter describing the distribution is introduced.A double generalized linear model,Poisson-Gamma model,is obtained by modeling the mean and divergence in the model.Secondly,in the case of complete data,we use the empirical likelihood method in the parameter model to construct the empirical likelihood ratio function of the unknown parameters in the Poisson-Gamma model and prove that the asymptotic distribution is the chi-square distribution,and then the mean parameter And the confidence interval of the divergence parameter.The validity and feasibility of the empirical likelihood method are obtained by comparing the coverage of the empirical likelihood method and the normal approximation method at the same level by data simulation.Thirdly,when the response variable is randomly absent,the k nearest distance method is used to fill the data set,and the data after the filling is modeled and the relevant parameter estimator is constructed.Finally,the comparison between the data simulation and the normal approximation method,It is effective and feasible to draw the filling method and the empirical likelihood method.