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中国科学院数学与系统科学研究院 王启华教授：Sufficient Dimension Reduction for Nonignorable Nonresponse

Sufficient dimension reduction (SDR) for nonignorable nonresponse  poses a challenge and  thus there is still no article on this problem. In the nonignorable case, methods derived under ignorable missing assumption are invalid and of serious estimation bias, especially when missing rate is high. In this article, a regression calibration based cumulative mean estimation (RC-CUME) procedure is proposed to recover central subspace $\mathcal S_ {Y|\mathbf X}$ with the help of a surrogate subspace. Asymptotic properties of RC-CUME are also investigated. To guide practical application, we construct two feasible surrogate subspaces and compare the proposed RC-CUME based on the two surrogate subspaces.

A modified BIC-type criterion is adopted to determine the structural dimension of $\mathcal S {y|\mathbf X}$. In addition, we extent our procedure to other SDR methods. Simulation studies are carried out to access the finite-sample performances of the proposed RC-CUME approach. A real data analysis is used to illustrate our method.