  This paper proposes a hierarchical method for estimating the location
parameters of a multivariate vector in the presence of missing data. At i th
step of this procedure an estimate of the location parameters for non-missing
components of the vector is based on combining the information in the subset of
observations with the non-missing components with updated estimates of the
location parameters from all subsets with even more missing components in an
iterative fashion. If the variance-covariance matrix is known, then the
resulting estimator is unbiased with the smallest variance provided missing
data are ignorable. It is also shown that the resulting estimator based on
consistent estimators of variance-covariance matrices obtains unbiasedness and
the smallest variance asymptotically. This approach can also be extended to
some cases of non-ignorable missing data. Applying the methodology to a data
with random dropouts yields the well known Kaplan-Meier estimator.
