Robust circular-circular correlation coefficient

Abstract

Many classical methods have been proposed to compute circular-circular correlation coefficients. However, these classical methods might be very sensitive to outliers in the data set. To date, no work has suggested a robust method to estimate a circular-circular correlation coefficient. The present paper aims to propose two robust methods to compute a circular-circular correlation coefficient when the circular data has outliers. The first method is computed based on the circular median, rMed, and the second on the circular trimmed mean, rTrim. A simulation study is conducted for two circular distributions: the wrapped normal and wrapped Cauchy distributions. The simulation and practical example show that the results of rMed are close to the results of classical methods. In contrast, the rTrim gives the best results and is the least affected by outliers, even with a high percentage of outliers.