Selection of Optimal Regression-like Equations for Circular Regression Model via Mallows’ $$C_p$$ and AIC Criteria

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.