A new outlier detection method for spherical data

In this study, we propose a new method to detect outlying observations in spherical data. The method is based on the k-nearest neighbours distance theory. The proposed method is a good alternative to the existing tests of discordancy for detecting outliers in spherical data. In addition, the new method can be generalized to identify a patch of outliers in the data. We obtain the cut-off points and investigate the performance of the test statistic via simulation. The proposed test performs well in detecting a single and a patch of outliers in spherical data. As an illustration, we apply the method on an eye data set.