Semi-parametric least-area linear-circular regression through M\"{o}bius transformation

TL;DR

This paper presents a semi-parametric regression model for angular responses with linear predictors, using a M"{o}bius transformation and an area-based loss function to effectively model complex circular data without strict distributional assumptions.

Contribution

It introduces a novel semi-parametric regression framework employing M"{o}bius transformation and an area-based loss, enhancing modeling flexibility for angular data.

Findings

Robust performance across von Mises and wrapped Cauchy distributions.

Effective modeling of cryptocurrency data (Bitcoin and Ethereum).

Eliminates the need for specific error distribution assumptions.

Abstract

This paper introduces a novel regression model designed for angular response variables with linear predictors, utilizing a generalized M\"{o}bius transformation to define the regression curve. By mapping the real axis to the circle, the model effectively captures the relationship between linear and angular components. A key innovation is the introduction of an area-based loss function, inspired by the geometry of a curved torus, for efficient parameter estimation. The semi-parametric nature of the model eliminates the need for specific distributional assumptions about the angular error, enhancing its versatility. Extensive simulation studies, incorporating von Mises and wrapped Cauchy distributions, highlight the robustness of the framework. The model's practical utility is demonstrated through real-world data analysis of Bitcoin and Ethereum, showcasing its ability to derive meaningful insights from complex data structures.