Univ. Heidelberg
Statistics Group   Institute of Applied Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Institute of Applied Mathematics Statistics of inverse problems Research Group
german english french



Publications
Cooperations
Research projects
Events
Teaching
Completed theses
People
Contact


Last edited on
Oct 10, 2022 by JJ
.

Discussion paper:
arXiv:2012.13332

Title:
Regression in nonstandard spaces with Fréchet and geodesic approaches

Author:
Christof Schötz

Abstract:
One approach to tackle regression in nonstandard spaces is 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. We compare these two approaches by using them to transform three of the most important regression estimators in statistics - linear regression, local linear regression, and trigonometric projection estimator - to settings where responses live in a metric space. The resulting procedures consist of known estimators as well as new methods. We investigate their rates of convergence in general settings and compare their performance in a simulation study on the sphere.

Comment / Contact
Markdown: formatting is possible. All comments are held for moderation.