2020/12/24 by Christof Schötz, Schötz, Christof · 2 citations
Mathematics · #62R20 #Advanced Statistical Methods and Models #FOS: Mathematics #Morphological variations and asymmetry #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2012.13332
openalex publication_date 2020/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.