Regression in Nonstandard Spaces with Fréchet and Geodesic Approaches

by   Christof Schötz, et al.

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.



There are no comments yet.


page 1

page 2

page 3

page 4


Robust Regression via Mutivariate Regression Depth

This paper studies robust regression in the settings of Huber's ϵ-contam...

Correlation Estimation System Minimization Compared to Least Squares Minimization in Simple Linear Regression

A general method of minimization using correlation coefficients and orde...

D-optimal designs for the Mitscherlich non-linear regression function

Mitscherlich's function is a well-known three-parameter non-linear regre...

Robust functional regression based on principal components

Functional data analysis is a fast evolving branch of modern statistics ...

Random Forests Weighted Local Fréchet Regression with Theoretical Guarantee

Statistical analysis is increasingly confronted with complex data from g...

Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression

The Shapley value solution concept from cooperative game theory has beco...

On a Projection Estimator of the Regression Function Derivative

In this paper, we study the estimation of the derivative of a regression...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.