Testing predictor effects in global Fréchet regression
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: hypothesis test, regression model
Session: IPS 728 - Recent Advances in Geometric and Object Data Analysis
Thursday 9 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
A challenging aspect of the analysis of random objects is the highly-varied and complex geometry of the spaces in which these objects lie. Fréchet regression is a framework that generalizes ordinary least squares regression to the case of random object responses. This extension results in a global model that requires no smoothing parameter to fit, thus potentially lending itself to conduct standard inferential procedures in this complex setting. When only a metric is assumed for the response space, the concept of a residual fades away, rendering usual inferential procedures obsolete. Beginning with the global hypothesis of no effect, we develop a test based on a generalized Fréchet $R^2$ coefficient, and derive its limiting null distribution. The performance of the test is then studied through simulation and real data analysis.