On diagnostic tests for circular regression models

Abstract

We present an overview of goodness-of-fit tests for circular data (see , e.g., Jammalamadaka et al. (2019) and Mardia & Jupp (2009)) and apply them to residuals of the circular-circular multiplicative regression model proposed in Kato et al. (2008). In this model, the regression curve is expressed as a Möbius transformation and the angular error is assumed to be distributed as a wrapped Cauchy distribution. We examine some theoretical properties of test statistics considered in this setting. Furthermore, we conduct a comprehensive Monte Carlo study to compare the performance of the presented tests. The application is illustrated on several real data sets.