Semi-parametric least-area linear-circular regression through Möbius transformation

This paper introduces a new area-based regression model where the responses are angular variables and the predictors are linear. The regression curve is formulated using a generalized M\"obius transformation that maps the real axis to the circle. A novel area-based loss function is introduced for parameter estimation, utilizing the intrinsic geometry of a curved torus. The model is semi-parametric, requiring no specific distributional assumptions for the angular error. Extensive simulation studies are performed with von Mises and wrapped Cauchy distributions as angular errors. The practical utility of the model is illustrated through real data analysis of two well-known cryptocurrencies, Bitcoin and Ethereum.