In this work, we develop a new theory and method for sufficient dimension
reduction (SDR) in single-index models, where SDR is a sub-field of supervised
dimension reduction based on conditional independence. Our work is primarily
motivated by the recent introduction of the Hellinger correlation as a
dependency measure. Utilizing this measure, we develop a method capable of
effectively detecting the dimension reduction subspace, complete with
theoretical justification. Through extensive numerical experiments, we
demonstrate that our proposed method significantly enhances and outperforms
existing SDR methods. This improvement is largely attributed to our proposed
method's deeper understanding of data dependencies and the refinement of
existing SDR techniques.

本文提出了一种新的理论和方法，用于单指数模型中的充分降维 (SDR)，SDR 是基于条件独立性的监督降维的一个子领域。利用 Hellinger 相关作为一种依赖度量，我们开发了一种能够有效检测降维子空间的方法，并给出了理论解释。通过大量的数值实验，我们证明了我们提出的方法明显优于现有的 SDR 方法。这种改进主要归因于我们提出的方法对数据依赖性的更深入理解和对现有 SDR 技术的改进。