Outlier Detection in a Circular Regression Model Using COVRATIO Statistic

Abstract

In this article, we model the relationship between two circular variables using the circular regression models, to be called JS circular regression model, which was proposed by Jammalamadaka and Sarma (1993). The model has many interesting properties and is sensitive enough to detect the occurrence of outliers. We focus our attention on the problem of identifying outliers in this model. In particular, we extend the use of the COVRATIO statistic, which has been successfully used in the linear case for the same purpose, to the JS circular regression model via a row deletion approach. Through simulation studies, the cut-off points for the new procedure are obtained and its power of performance is investigated. It is found that the performance improves when the resulting residuals have small variance and when the sample size gets larger. An example of the application of the procedure is presented using a real dataset.

Keywords:

• Circular regression
• COVRATIO
• Influential observation
• Outlier
• von Mises distribution

Mathematics Subject Classification:

• Primary 62H11; Secondary 62J20

Acknowledgments

The authors are most grateful to the Associate Editor and referees for their thorough reading and valuable suggestions, which led to a substantial improvement of the article.