Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random

Abstract

Dimension reduction methods are useful for handling high-dimensional data. It is a common situation that responses of some subjects are not observed in practice. Generally, the missingness carries additional information about the central subspace. Here we propose a two-stage procedure known as the fusion-refinement (FR) procedure. In the first stage, we obtain a subspace including the central subspace by fusing information on regression and missingness. In the second stage, we refine the obtained subspace to recover the central subspace by imputation method. We use sliced inverse regression to illustrate the FR procedure. We conduct simulation studies, and suggest a data-driven procedure to choose from the complete-case analysis and the FR procedure for a purpose of a real application. A real data analysis is used to illustrate our methods.