On sliced inverse regression with missing values

Abstract

ABSTRACTTo deal with predictors missing at random in sufficient dimension reduction, IPW-SIR (Li and Lu (2008), ‘Sufficient dimension reduction with missing predictors’, Journal of American Statistical Association, 103, 882–831) combines inverse probability weighting and sliced inverse regression (Li (1991), ‘Sliced inverse regression for dimension reduction’ (with discussion). Journal of the American Statistical Association, 86, 316–342). IPW-SIR is extended to handle response missing at random in this paper. The -consistency and asymptotic normality of the proposed estimator are established. Furthermore, IPW-SIR is adapted to deal with the challenging case when both the response and the predictors are missing at the same time. The superior performances of the proposed estimators over existing methods are demonstrated through simulation studies as well as analysis of a HIV clinical trial data.