论文标题
非标准空间中的非参数回归
Nonparametric Regression in Nonstandard Spaces
论文作者
论文摘要
非参数回归设置被视为实现的协变量和度量空间的响应。可以通过Fréchet回归接近此设置，其中每个点的回归函数的值是通过根据估计的目标函数计算得出的fréchet平均值来估算的。第二种方法是测量回归，该回归是基于将大地测量学拟合到最小二乘法对观测的基础。这些方法用于将统计中最重要的两个非参数回归估计器转换为度量设置 - 局部线性回归估计器和正交串联投影估计器。结果过程包括已知的估计器以及新方法。我们在一般环境中研究了它们的收敛速度，并在对球体的仿真研究中进行了比较。
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fréchet regression, where the value of the regression function at each point is estimated via a Fréchet 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.
