Statistical Inference For Generalized Linear Models With Responses Variables Missing At Random

Generalization of the classical linear models------generalized linear models, Successfully dealt with the complicated nonlinear relationship between the dependent variable and the independent variables, overcame the limitations of the classical linear model. The phenomenon of lack of data is inevitably exist in various fields, throwing away the missing data may lost the information contained in the data missing and decrease the rate of accurate. So, how to effective access to the information in the missing data, has become a hotspot in current research. Since Owen put forward the empirical likelihood method, because of its many good properties, such as:transform invariance, mergence, Bartlett corrective, incredible domain shape is determined by the data completely, loved by the majority of scholars, therefore it is widely used in various kinds of data research.Based on the background of data missing at random, the model checking method of generalized linear models and the empirical likelihood inference of generalized linear models are studied. In the model checking method of generalized linear models, this paper respectively use imputation and inverse marginal probability weighted approaches established two kinds of "complete data "sets. Based on the two kinds of complete data sets, We have established two kinds of empirical process-based tests to verify whether our generalized linear model is reasonable. we also use the non-parameter Monte Carlo method to approximate the asymptotic distribution of the statistic under null hypothesis. With respect to empirical likelihood inference of generalized linear models. using the empirical likelihood method, we constructed a series of empirical likelihood ratio function of unknown parameters and the mean, and proved that the empirical log likelihood ratio function obeys asymptotic chi square distribution. So we can draw the confidence domain of the unknown parameters and the mean. in addition, we also got the estimator of the unknown parameters and the mean, and proved that these estimators follow normal distribution. In the simulation study, we use inverse marginal probability weighted approaches to estimate the empirical likelihood confidence regions of the unknown parameters and the mean, and estimated the normal approximation of the unknown parameters and the mean. At last, by comparing the average length and coverage rate of them, we found that under the method of inverse marginal probability weighted approaches, the empirical likelihood confidence regions have high precision than other methods.