Adapting Akaike information criterion to multiple circular regression

Circular data analysis has attracted much interest in various disciplines, as can be seen from a multitude of papers, as well as books such as Mardia and Jupp (Citation2000) and Jammalamadaka and SenGupta (Citation2001). In this article, we focus on the issue of selecting optimal regressors in a multiple circular regression problem, using ideas similar to the Akaike information criterion (AIC) that is widely used in the context of linear regression, and develop pertinent variations of it. A “Circular Akaike Information Criterion” (CAIC) and a robust version of it, which we call the “Robust Circular Akaike Information Criterion (RCAIC)” are proposed here and used to select the optimal regressors in multiple circular regression contexts. The robustness study also examines the finite-sample breakdown point and the influence function for the CAIC criterion. The performance of the proposed criteria is evaluated, first using extensive simulation studies, and then applied to a real dataset in a medical study. The results reveal that in both uncontaminated and contaminated data sets, the criteria CAIC and RCAIC are quite efficient in selecting optimal regressors in such multiple circular regression models.