Estimation of the mean when data contain non-ignorable missing values from a random effects model

This paper is concerned with the inference of incomplete data when the missing data process is non-ignorable in the sense of Rubin (Biometrica 38 (1982) 963-974). With the random effects model and the proposed missing data process, the conditions missing at random (MAR) and distinct parameters (DP) are discussed. The impact of the missing data is illustrated by the asymptotic bias of the sample mean based on only the observed data and ignoring the missing data process. Maximum likelihood and moment estimators of the marginal mean are obtained.