Surrogate space based dimension reduction for nonignorable nonresponse

Abstract Sufficient dimension reduction (SDR) for nonignorable nonresponse poses a challenge and the literature about this issue is very rare. In the nonignorable case, the SDR methods developed for ignorable missing data generally yield serious estimation bias and thus are invalid. A regression-calibration-based cumulative mean estimation (RC-CUME) procedure is proposed to recover the central subspace (CS) with the aid of a surrogate subspace. Asymptotic properties of the RC-CUME are investigated. A modified BIC-type criterion is used to determine the structural dimension of the CS. Some extensions to other SDR methods are presented. Simulation studies are conducted to access the finite-sample performance of the proposed RC-CUME approach, and a real data set is analyzed for illustration.