Nonparametric regression in nonstandard spaces
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 fun...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
27 September 2022
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| In: |
Electronic journal of statistics
Year: 2022, Volume: 16, Issue: 2, Pages: 4679-4741 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/22-EJS2056 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1214/22-EJS2056 Verlag, lizenzpflichtig, Volltext: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-16/issue-2/Nonparametric-regression-in-nonstandard-spaces/10.1214/22-EJS2056.full 
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| Author Notes: | Christof Schötz |
MARC
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| 520 | |a 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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