AbstractThere are many practical situations where observation of the primary variableYfor individuals in a population is incomplete and depends on some auxiliary variablesXthat are potentially correlated withY. We consider parameter estimation for the distribution ofYwith the incomplete data, without specifying the underlying association betweenYandX. The approach is based on a class of pseudoscore functions using available information ofX. We demonstrate the consistency and asymptotic normality of the estimators and study their finite‐sample properties in various situationsviasimulation. The methodology is illustrated by an example involving kindergarten readiness skills in children with sickle cell disease. Copyright © 2006 John Wiley & Sons, Ltd.