Missing data analysis with sufficient dimension reduction

This article develops a two-step procedure for estimating the unknown parameters in a model that contains a fixed but large number of covariates, more moment conditions than unknown parameters, and responses that are missing at random. We propose a sufficient dimension reduction method to be implemented in the first step and prove that the method is asymptotically valid. In the second step, we apply three well-known missing data handling mechanisms together with the generalized method of moments to the reduced-dimensional subspace to obtain estimates of unknown parameters. We investigate the theoretical properties of the proposed methods, including the effects of dimension reduction on the asymptotic distributions of the estimators. Our results refute a claim in an earlier study that dimension reduction yields the same asymptotic distributions of estimators as when the reduced-dimensional structure is the true structure. We illustrate our method by way of a simulation study and a real clinical trial data example.