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.

翻译：本研究针对单指标模型中的充分降维问题，提出了一种新的理论与方法。充分降维是基于条件独立性的监督降维子领域。我们的研究主要受到近期提出的Hellinger相关性作为依赖度量的启发。利用该度量，我们开发了一种能够有效检测降维子空间的方法，并提供了完整的理论证明。通过大量数值实验，我们证明所提出的方法显著增强并超越了现有的充分降维方法。这一改进主要归因于我们提出的方法对数据依赖关系更深入的理解以及对现有充分降维技术的改进。