A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated via a Fr\'echet mean calculated from an estimated objective function. A second approach is geodesic regression, which builds upon fitting geodesics to observations by a least squares method. These approaches are applied to transform two of the most important nonparametric regression estimators in statistics to the metric setting -- the local linear regression estimator and the orthogonal series projection estimator. The resulting procedures consist of known estimators as well as new methods. We investigate their rates of convergence in a general setting and compare their performance in a simulation study on the sphere.

翻译：在考虑非对称回归设置时,考虑的是实际价值的共变法和来自计量空间的反应。我们可以通过Fr\'echet回归法来看待这一设定,在这种回归法中,每个点的回归函数值通过从估计的客观函数中计算得出的Fr\'echet平均值来估算。第二个方法是大地测量回归法,它建立在与以最小方位方法进行观测相适应的大地测量法之上。这些方法用于将统计中两个最重要的非参数回归估计值转换到基准设置 -- -- 即局部线性回归估计值和正方位序列预测估计估计值。由此产生的程序由已知的估算数和新方法组成。我们在一般情况下调查其趋同率,并在关于球体的模拟研究中比较其性能。