Variable Selection for Global Fr\'Echet Regression

• Activity Number: 201 - Nonparametric Statistics Student Paper Competition Presentations
• Type: Topic-Contributed
• Date/Time: Tuesday, August 10, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Danielle C. Tucker* and Yichao Wu and Hans-Georg Müller
• Companies: University of Illinois at Chicago and University of Illinois at Chicago and University of California, Davis
• Keywords: Metric space valued data; Euclidean predictors; Important predictors; Ridge regression; Spherical data; Network data

Abstract

Global Fr\'echet regression is an extension of linear regression to cover more general types of responses, such as distributions, networks and manifolds, which are becoming more prevalent. In such models, predictors are Euclidean while responses are metric space valued. Predictor selection is of major relevance for regression modeling in the presence of multiple predictors but has not yet been addressed for Fr\'echet regression. Due to the metric space valued nature of the responses, the Fr\'echet regression model does not feature model parameters, and this lack of parameters makes it a major challenge to extend existing variable selection methods for linear regression to global Fr\'echet regression. In this work, we address this challenge and propose a novel variable selection method that overcomes it and has good practical performance. We provide theoretical support and demonstrate that the proposed variable selection method achieves selection consistency. Numerical examples and data illustrations demonstrate the finite sample performance of the proposed method.