Pseudoscore-based estimation from biased observations

There are many practical situations where observation of the primary variable Y for individuals in a population is incomplete and depends on some auxiliary variables X that are potentially correlated with Y. We consider parameter estimation for the distribution of Y with the incomplete data, without specifying the underlying association between Y and X. The approach is based on a class of pseudoscore functions using available information of X. We demonstrate the consistency and asymptotic normality of the estimators and study their finite-sample properties in various situations via simulation. The methodology is illustrated by an example involving kindergarten readiness skills in children with sickle cell disease.