Abstract
The problem of choosing the best regressors to fit the circular regression data has not been addressed. We focus on the problem of finding the optimal regression-like equations (ORLE) in the Sarma and Jammalamadaka (SJ) circular regression model (Sarma and Jammalamadaka 1993). First, the issues of under-fitting and over-fitting of regression equations in the SJ model are addressed. Then, we extend Mallows' C-p and AIC and their robust versions to the SJ circular regression model. A simulation study is used to investigate the performance of the proposed criteria. Results showed that robust circular Mallows' C-p and AIC are effective in selecting an accurate ORLE for circular regression models in both the clean and contaminated data sets. An application of the proposed procedures is discussed using a real medical data set.