On the influential points in the functional circular relationship models

If the interest is to calibrate two instruments then the functional relationship models are more appropriate than regression models. fitting a straight line when both variables are circular and subject to errors has not received much attention. in this paper,we consider the problem of detecting influential points in two functional relationship models for circular variables. the first is developed based on the simple circular regression model,demoted by (sc),while the second is derived from the complex linear regression model and denoted by (cl). the covariance matrices are derived and then the covratio statistics are formulated for both models. the cut-off points are obtained and the power of performance is examined via simulation studies. the performance of covratio statistics depends on the concentration of error,sample size and level of contamination. in the case of the linear relationship between two circular variables,covratio statistics of the (sc) model performs better than the (cl). furthermore,a novel diagram,the so-called spoke plot,is utilized to detect possible influential points. for illustration purposes,the proposed procedures are applied on real data of wind directions measured by two different instruments. covratio statistic and the spoke plot were able to identify two observations as influential points.