Open Access
2022 Nonparametric regression in nonstandard spaces
Christof Schötz
Author Affiliations +
Electron. J. Statist. 16(2): 4679-4741 (2022). DOI: 10.1214/22-EJS2056


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.


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Christof Schötz. "Nonparametric regression in nonstandard spaces." Electron. J. Statist. 16 (2) 4679 - 4741, 2022.


Received: 1 November 2021; Published: 2022
First available in Project Euclid: 27 September 2022

MathSciNet: MR4489238
zbMATH: 07603096
Digital Object Identifier: 10.1214/22-EJS2056

Primary: 62G08 , 62R20

Keywords: Fréchet mean , Fréchet regression , geodesic regression , metric space , Nonparametric regression

Vol.16 • No. 2 • 2022
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