A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia's model are studied via simulations. For illustration, we apply the procedure on circadian data.
Rambli, A., Abuzaid, A. H. M., Bin Mohamed, I., & Hussin, A. G. (2016). Procedure for detecting outliers in a circular regression model. PLoS ONE, 11(4). https://doi.org/10.1371/journal.pone.0153074