Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean responses, our work introduces a novel statistical method for handling random objects with circular predictors. We concentrate on local constant and local linear Fr\'echet regression, providing rigorous proofs for the upper bounds of both bias and stochastic deviation of the estimators under mild conditions. This research lays the groundwork for broadening the application of Fr\'echet regression to scenarios involving non-Euclidean covariates, thereby expanding its utility in complex data analysis.

翻译：弗雷歇回归将线性回归的原理推广至度量空间中的响应变量。尽管该方法主要关注欧几里得预测变量与非欧几里得响应之间的关系，但本研究提出了一种处理具有圆形预测变量的随机对象的新统计方法。我们聚焦于局部常数与局部线性弗雷歇回归，在温和条件下严格证明了估计量的偏差与随机偏差的上界。本研究为将弗雷歇回归的应用拓展至涉及非欧几里得协变量的场景奠定了基础，从而增强了其在复杂数据分析中的实用性。