Fr\'echet global regression is extended to the context of bivariate curve stochastic processes with values in a Riemannian manifold. The proposed regression predictor arises as a reformulation of the standard least-squares parametric linear predictor in terms of a weighted Fr\'echet functional mean. Specifically, in our context, in this reformulation, the Euclidean distance is replaced by the integrated quadratic geodesic distance. The regression predictor is then obtained from the weighted Fr\'echet curve mean, lying in the time-varying geodesic submanifold, generated by the regressor process components involved in the time correlation range. The regularized Fr\'echet weights are computed in the time-varying tangent spaces. The weak-consistency of the regression predictor is proved. Model selection is also addressed. A simulation study is undertaken to illustrate the performance of the spherical curve variable selection algorithm proposed in a multivariate framework.

翻译：Fr\'echet 全局回归扩展至具有里曼尼方块数值的双轨曲线切换过程。 拟议的回归预测器以加权 Fr\' echet 函数平均值重塑了标准的最小平方线性线性预测器。 具体地说, 在我们的重拟中, 欧几里德距离被集成的二次测深距离所取代。 回归预测器取自加权的Fr\' echet 曲线平均值, 位于时间变化的大地测量子下方, 由时间相关范围的回归进程组成部分生成。 常规化的 Fr\\' echet 重量在时间变化的正切空格中计算。 回归预测器的不一致性得到了证明。 模型选择也被处理。 进行模拟研究是为了说明在多变量框架中提议的球曲线变量选择算法的性。