Irical Likelihood For Generalized Linear Models With Nonignorable Missing Data

In biomedical, education and economics studies, missing data are common. These subjects are hot topics in the statistical study. At present most of the studies home and abroad on statistical inference for these problems under ignorable missing assumption. But some practical problems(such as privacy problems) lead to more and more missing data nonignorable. The existing statistical inference approachs for ignorable missing data can not be used to deal with nonignorable missing data and produce estimates that can not effective. Therefore, researching a Generalized Linear model with nonignorable missing data is very meaningful. However, since the nonignorable missing data becomes very difficult, the problem has not a very good development.This paper on the basis of the Generalized Linear model with the nonignorable missing data, use the empirical likelihood methods for parameter estimation. The main works include:(1) According to the nonignorable missing data, the missing probability function is estimated by using the propensity score adjustment methods, and the estimation is consistency.(2) The unbiased estimating equations is established by using the inverse probability weighted theory. With or not with the auxiliary information, use the empirical likelihood methods for parameter estimation, and the parameter estimators are consistent and asymptotically normal.(3) Through simulation studies and a real example, verify the efficiency and robustness of the proposed method.