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<p>In this paper, the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds. The authors rigorously establish statistical properties of the estimators, providing formal proofs of their consistency and asymptotic behaviors. The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.</p>

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Nonlinear Sufficient Dimension Reduction for Metric Space Objects

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Xueyan Huang,
  • Yunchen Li,
  • Chao Ying,
  • Zhou Yu

摘要

In this paper, the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds. The authors rigorously establish statistical properties of the estimators, providing formal proofs of their consistency and asymptotic behaviors. The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.