Year: 2024
Type: preprint
Abstract: Fréchet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean responses, our work introduces a novel statistical method for handling random objects with circular predictors. We concentrate on local constant and local linear Fréchet regression, providing rigorous proofs for the upper bounds of both bias and stochastic deviation of the estimators under mild conditions. This research lays the groundwork for broadening the application of Fréchet regression to scenarios involving non-Euclidean covariates, thereby expanding its utility in complex data analysis.
Source: arXiv (Cornell University)
Authors: Im, Chang Jun, Jeon, Jeong Min
Institutions: Seoul National University, Ewha Womans University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403585443