Local Fr\'echet regression with circular predictors

TL;DR

This paper develops a new statistical method for Fréchet regression with circular predictors, providing theoretical guarantees and expanding its applicability to non-Euclidean covariates in complex data analysis.

Contribution

It introduces local constant and linear Fréchet regression methods for circular predictors with rigorous bias and deviation bounds, broadening Fréchet regression's scope.

Findings

Established upper bounds for bias and stochastic deviation.

Extended Fréchet regression to circular predictor variables.

Provided theoretical foundations for future applications.

Abstract

Fr\'echet 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 Fr\'echet 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 Fr\'echet regression to scenarios involving non-Euclidean covariates, thereby expanding its utility in complex data analysis.