Dimension reduction with missing response at random

When there are many predictors, how to efficiently impute responses missing at random is an important problem to deal with for regression analysis because this missing mechanism, unlike missing completely at random, is highly related to high-dimensional predictor vectors. In sufficient dimension reduction framework, the fusion-refinement (FR) method in the literature is a promising approach. To make estimation more accurate and efficient, two methods are suggested in this paper. Among them, one method uses the observed data to help on missing data generation, and the other one is an ad hoc approach that mainly reduces the dimension in the nonparametric smoothing in data generation. A data-adaptive synthesization of these two methods is also developed. Simulations are conducted to examine their performance and a HIV clinical trial dataset is analyzed for illustration.