A robust inverse regression estimator

A family of dimension reduction methods was developed by Cook and Ni [Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Amer. Statist. Assoc. 100, 410-428.] via minimizing a quadratic objective function. Its optimal member called the inverse regression estimator (IRE) was proposed. However, its calculation involves higher order moments of the predictors. In this article, we propose a robust version of the IRE that only uses second moments of the predictor for estimation and inference, leading to better small sample results.