J4 ›› 2011, Vol. 46 ›› Issue (4): 17-22.

• Articles • Previous Articles     Next Articles

Linear functionals semiparametric dimension reduction inference with missing data

ZHU Li-ping1,2, SHAO Wei1   

  1. 1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China;
    2. Department of Mathematics,  Changji College, Changji 831100, Xinjiang, China
  • Received:2010-12-01 Published:2011-04-21


A semiparametric dimension reduction method is proposed to reconcile the nonparametric regression approach and the model-based approaches in estimating linear functionals with missing data. The linear functionals are estimated through nonparametric functionals estimation, where the dimension is reduced by a parametric working index. The proposed estimator is robust to model misspecification: it is always consistent either the selected probability is correctly specified or the working index can recover the conditional linear functionals given the covariates. In addition, when both above conditions are satisfied, the proposed estimator attains the optimal efficiency.

Key words: linear functionals; missing data; dimension reduction

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