Statistica Sinica 28 (2018), 2125-2148
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. That 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 data analyses.
Key words and phrases: Missing data mechanism, nonignorable missing data, penalized pairwise pseudo likelihood, regularization, selection consistency, variable selection.