Sufficient dimension reduction and prediction in regression: Asymptotic results

We consider model-based sufficient dimension reduction for generalized linear models and prove the consistency and asymptotic normality of the prediction estimator studied empirically for the normal case by Adragni and Cook (2009) when a sample version of the sufficient dimension reduction is used. Moreover, we provide a formula for the prediction that does need require explicitly computing the reduction. (C) 2018 Elsevier Inc. All rights reserved.