A new estimator for efficient dimension reduction in regression

In this paper we propose a new estimator for efficient dimension reduction in regression, based on the work in Luo et al. (2014). Previous efficient estimators have been proposed by multiple authors, however under additional restrictive assumptions on the conditional variance of the response variable given the predictor vector. These assumptions also complicate the implementation. In contrast, the new estimator employs no such assumptions, and thus is far more applicable and more convenient to use. By an extended double-robustness property, it reaches asymptotic efficiency under fairly general conditions. Its finite-sample effectiveness is further illustrated by simulation studies and a real data example.