Enhanced Outlier Detection in Linear-Circular Regression Using Circular Distance and Mean Resultant Length

Abstract

In the study of outlier identification in linear-circular regression, two new methods are proposed. By calculating the circular distance of each erroneous value and using the mean resultant length for outlier identification, these methods aim to enhance the precision and reliability of outlier detection. Their effectiveness will be assessed through comprehensive simulations on datasets with and without outlier contamination, comparing them with the previous method. Additionally, the methods were tested on real-world data, specifically wind speed and wind direction data, to further validate their practical applicability. Three metrics are used to evaluate their performance: the probability of correctly identifying all outliers, the masking effect, and the swamping effect. While occasional misclassification of inliers as outliers is possible, the results indicate that both proposed methods demonstrate strong overall performance.