Sufficient dimension reduction in regressions with missing predictors

Existing sufficient dimension reduction methods often resort to the complete-case analysis when the predictors are subject to missingness. The complete-case analysis is inefficient even with the missing completely at random mechanism because all incomplete cases are discarded. In this paper, we introduce a nonparametric imputation procedure for semiparametric regressions with missing predictors. We establish the consistency of the nonparametric imputation under the missing at random mechanism that allows the missingness to depend exclusively upon the completely observed response. When the missingness depends on both the completely observed predictors and the response, we propose a parametric method to impute the missing predictors. We demonstrate the estimation consistency of the parametric imputation method through several synthetic examples. Our proposals are illustrated through comprehensive simulations and a data application.