Intrinsic Riemannian Functional Sufficient Dimension Reduction and Beyond
针对黎曼随机过程预测变量和度量空间响应，提出两种内蕴黎曼函数充分降维方法，理论证明无偏性和最优收敛率，并用于球面和Wasserstein函数数据。
This paper focuses on linear sufficient dimension reduction with Riemannian random processes as predictors and complex random objects in a metric space as responses. We propose two novel methods—Intrinsic Riemannian Functional Weighted Inverse Regression Ensemble (iRF-WIRE) and Intrinsic Riemannian Functional Weighted Directional Regression (iRF-WDR)—to recover the central subspace. These methods can be readily extended to Wasserstein functional predictors. We establish their theoretical properties, including unbiasedness and optimal convergence rates, and conduct extensive simulation studies to assess their performance. Finally, we demonstrate the broad applicability of the proposed methods through two real-world datasets involving spherical functional data and Wasserstein functional data.