Sufficient Dimension Reduction under Dimension-reduction-based Imputation with Predictors Missing at Random

Abstract

Abstract:In some practical problems, a subset of predictors are frequently subject to missingness, especially when the dimension of the predictors is high. For this case, the standard sufficient dimension reduction (SDR) methods cannot be applied directly to avoid the curse of dimensionality. A dimension-reductionbased imputation method is developed in this article such that any of spectraldecomposition-based SDR methods for full data is applicable to the case of predictors missing at random. The sliced inverse regression (SIR) is used to illustrate this procedure. The proposed dimension-reduction-based imputation estimator of the candidate matrix for SIR, termed as DRI-SIR estimator, is asymptotically normal under some mild conditions and hence the resulting estimator of the central subspace is root n consistent. The finite sample performance of the proposed method is evaluated through comprehensive simulations and a real data set is analyzed for illustration.

Semiparametric recovery of central dimension reduction space with nonignorable nonresponse

“…Zhu, Wang, and Zhu (2012) developed a nonparametric imputation method for SIR with covariate MAR, but the method can be applied only when the missing data depend exclusively on the fully observed response. Wang and Wang (2019) proposed a nonparametric imputation method for SIR that has broader applicability than that of Zhu et al (2012). The thrust of their method entails using SIR to construct low‐dimensional linear combinations of the completely observed data to obtain dimension‐reduction‐based imputed estimates.…”