  We introduce a novel approach to estimation problems in settings with missing
data. Our proposal -- the Correlation-Assisted Missing data (CAM) estimator --
works by exploiting the relationship between the observations with missing
features and those without missing features in order to obtain improved
prediction accuracy. In particular, our theoretical results elucidate general
conditions under which the proposed CAM estimator has lower mean squared error
than the widely used complete-case approach in a range of estimation problems.
We showcase in detail how the CAM estimator can be applied to $U$-Statistics to
obtain an unbiased, asymptotically Gaussian estimator that has lower variance
than the complete-case $U$-Statistic. Further, in nonparametric density
estimation and regression problems, we construct our CAM estimator using kernel
functions, and show it has lower asymptotic mean squared error than the
corresponding complete-case kernel estimator. We also include practical
demonstrations throughout the paper using simulated data and the Terneuzen
birth cohort and Brandsma datasets available from CRAN.
