We provide the first regression framework that simultaneously accommodates responses taking values in a general metric space and predictors lying on a general torus. We propose intrinsic local constant and local linear estimators that respect the underlying geometries of both the response and predictor spaces. Our local linear estimator is novel even in the case of scalar responses. We further establish their asymptotic properties, including consistency and convergence rates. Simulation studies, together with an application to real data, illustrate the superior performance of the proposed methodology.

翻译：我们提出了首个回归框架，该框架同时适用于取值于一般度量空间的响应变量和位于一般环面上的预测变量。我们提出了尊重响应空间与预测变量空间底层几何结构的固有局部常数与局部线性估计量。即使在标量响应的情况下，我们的局部线性估计量也具有新颖性。我们进一步建立了它们的渐近性质，包括一致性与收敛速率。模拟研究以及实际数据应用展示了所提方法的优越性能。