SUFFICIENT DIMENSION REDUCTION UNDER DIMENSION-REDUCTION-BASED IMPUTATION WITH PREDICTORS MISSING AT RANDOM

In some practical problems, a subset of predictors may be subject to missingness, especially when the dimension of the predictors is high. In this case, the standard sufficient dimension-reduction (SDR) methods cannot be applied directly to avoid the curse of dimensionality. Therefore, a dimension-reduction-based imputation method is developed such that any spectral-decomposition-based SDR method for full data can be applied to the case where predictors are missing at random. The sliced inverse regression (SIR) technique is used to illustrate this procedure. The proposed imputation estimator of the candidate matrix for the SIR, called the DRI-SIR estimator, is asymptotically normal under some mild conditions. Hence, the resulting estimator of the central subspace is root-n consistent. The finite-sample performances of the proposed method is evaluated through comprehensive simulations and real data are analyzed in an application of the method.