A new approach in modelling the circular data: circular ridge estimator

Different regression models that use circular data supported on the unit circle are rare. Regression parameters for circular data have mostly been estimated using the least-squares method. This paper addresses multicollinearity between the circular regressors. The ridge estimator is suggested as an alternative to the least-squares estimator in circular-linear regression model. The models fitted by the circular least-squares and circular ridge estimators are compared on real and simulated datasets. The mean squared error and the coefficient of determination are used to assess the models' adequacy. The findings demonstrated that the fitted models might not be significant if the circularity of the data is ignored. Circular regression on circular data shows the model to be significant. Although the two estimators' coefficients of determination for circular models are quite close, the circular ridge estimator with the optimum biasing parameter has a smaller scalar mean square error than the circular least-squares estimator.