Title: Penalized pairwise pseudo likelihood for variable selection with nonignorable missing data,
Abstract: The regularization approach for variable selection was well developed for a
completely observed data set in the past two decades. In the presence of
missing values, this approach needs to be tailored to different missing data
mechanisms. In this paper, we focus on a flexible and generally applicable
missing data mechanism, which contains both ignorable and nonignorable missing
data mechanism assumptions. We show how the regularization approach for
variable selection can be adapted to the situation under this missing data
mechanism. The computational and theoretical properties for variable selection
consistency are established. The proposed method is further illustrated by
comprehensive simulation studies and real data analyses, for both low and high
dimensional settings.