  We investigate methods for penalized regression in the presence of missing
observations. This paper introduces a method for estimating the parameters
which compensates for the missing observations. We first, derive an unbiased
estimator of the objective function with respect to the missing data and then,
modify the criterion to ensure convexity. Finally, we extend our approach to a
family of models that embraces the mean imputation method. These approaches are
compared to the mean imputation method, one of the simplest methods for dealing
with missing observations problem, via simulations. We also investigate the
problem of making predictions when there are missing values in the test set.
