Using Auxiliary Data for Binomial Parameter Estimation with Nonignorable Nonresponse

摘要

Nonignorable nonresponse is a nonresponse mechanism that depends on the values of the variable having nonresponse. When an observed data of a binomial distribution suffer missing values from a nonignorable nonresponse mechanism, the binomial distribution parameters become 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 focus on the model when the nonresponse is nonignorable and we consider to use the auxiliary data to improve identifiability; furthermore, we derive the maximum likelihood estimator (MLE) for the binomial proportion and its associated variance. We present results for an analysis of real-life data from the SARS study in China. Finally, the simulation study shows that the proposed method gives promising results.