Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regression in Nonstandard Spaces with Fr\'echet and Geodesic Approaches   One approach to tackle regression in nonstandard spaces is Fr\'echet
regression, where the value of the regression function at each point is
estimated via a Fr\'echet 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.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph