Abstract: This paper provides a regression model in which both covariates and responses are angular variables. The regression curve is expressed as a form of the Möbius circle transformation. The angular error is assumed to follow a wrapped Cauchy or, equivalently, circular Cauchy distribution. A bivariate circular distribution is proposed to model our circular regression. Some properties of the regression, including estimation and testing procedures, are obtained. The proposed methods are applied to marine biology and wind direction data.
Key words and phrases: Bivariate circular distribution, Möbius transformation, wrapped Cauchy distribution.