Dimension Reduction for Frechet Regression.

ABSTRACT: With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fréchet regression model (Peterson & Müller 2019) provides a promising framework for regression analysis with metric space-valued responses. In this paper, we introduce a flexible sufficient dimension reduction (SDR) method for Fréchet regression to achieve two purposes: to mitigate the curse of dimensionality caused by high-dimensional predictors, and to provide a visual inspection tool for Fréchet regression. Our approach is flexible enough to turn any existing SDR method for Euclidean ( X,Y ) into one for Euclidean X and metric space-valued Y . The basic idea is to first map the metric space-valued random object Y

SUBMITTER: Zhang Q 

PROVIDER: S-EPMC11810122 | biostudies-literature | 2024

REPOSITORIES: biostudies-literature