Fréchet kNN-based sufficient dimension reduction

Abstract

In this paper, we introduce two Fréchet inverse regression methods with kernel bandwidths determined by $k$ nearest neighbors, designed to achieve sufficient dimension reduction for a metric space-valued response and Euclidean predictors. A key advantage of the proposals lies in their ability to effectively preserve the intrinsic information of the metric space-valued response. We establish the asymptotic normality of these methods through rigorous theoretical proofs. Additionally, simulations and a real data example are provided to validate the performance and practical applicability of the proposed methods.