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The paper attempts to address the robustness issues in circular–circular regression. The Möbius transformation-based link function for circular–circular regression is considered. Defining the concept of breakdown point in this context, the robustness issues of the estimators in this model are discussed. Maximum trimmed cosine estimator in this context is considered and the breakdown point of the estimator is calculated. An exact polynomial time algorithm is then proposed for the computation of the estimator which makes the methodology useful and readily applicable for empirical datasets. Simulation studies show that the estimator is robust with respect to the outliers. An analysis of real data is performed to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

With reference to a real data on cataract surgery, we discuss the problem of zero-inflated circular-circular regression when both covariate and response are circular random variables and a large proportion of the responses are zeros. The regression model is proposed, and the estimation procedure for the parameters is discussed. Some relevant test procedures are also suggested. Simulation studies and real data analysis are performed to illustrate the applicability of the model. [ABSTRACT FROM AUTHOR]

In this article, we consider the circular–circular regression model using Möbius transformation. We first consider the model provided by Kato et al. (2008) for only one circular regressor and prove the identifiability of the model. After that, a methodology is discussed to reduce the prediction error of this model. We then introduce the two multiple circular–circular regression models with multiple circular regressors. We prove the identifiability of the models and discuss their geometry. We then discuss the parameter estimation procedure followed by simulation study. The methodologies are illustrated by some real datasets. [ABSTRACT FROM AUTHOR]