Binomial parameter estimation with nonignorable missing data

When an observation of a binomial distribution suffers missing data from a nonignorable nonresponse mechanism, the binomial distribution parameters becomes to be unidentifiable without any other auxiliary information or assumption. To address the problems of non-identifiability, existing methods mostly based on the log-linear regression model. In this article, we consider to use the auxiliary data to improve identifiability, further we derive the maximum likelihood estimator(MLE) for the binommial proportion and its associated variance, the simulation study shows that the proposed method gives promising results.