Robust estimators for circular regression models

Abstract The problem of robust estimation in circular regression models has not been studied well. This paper considers the JS circular regression model due to its interesting properties and its sensitivity for existence and detection of outliers. We extend the robust estimators such as M-estimation, least-trimmed squares (LTS), and least-median squares (LMS) estimators, which have been successfully used in the linear regression models, to the JS circular regression model. The robustness of the proposed estimators are studied through its influence function, and via simulation study. The results show that the proposed robust circular M-estimation is effective in estimating circular models' parameters in the presence of vertical outliers. However, circular LTS and LMS are highly robust estimators in case of circular leverage points. An application of the proposed robust circular estimators is illustrated using a real eye data set.