Identifying Outlier Observations in Linear - Circular Regression Model

Authors
Seyede Sedighe Azimi
Mohammad Reza Farid Rohani
10.52547/mmr.6.1.99
Abstract
One way to identify outlier observations in regression models, is to measure the difference between the observations and their expected values under fitted model. This identification in circular regression, is possible by using of a circular distance. In this paper, the Difference of Means Circular Error statistic that was introduced by ‎Abuzaid et al. [1] for outlier detection in simple circular regression, is applied in linear-circular regression model and the cut-off points of this statistic are obtained by Monte Carlo simulations. In addition, the performance of this statistic is investigated with some simulation studies. Finally, this statistic is applied to identify outlier observations in speed and direction wind data set recorded at Mehrabad weather station in Tehran with parametric Bootstrap simulation method../files/site1/files/61/10.pdf
Keywords
Linear - Circular regression model
Outlier observation
Difference of means circular Error
1. Abuzaid A. H., Hussin A. G., Mohamed I. ‎B., "Detection of outliers in simple circular regression models using the mean circular error statistic"‎, Journal of Statistical Computation and Simulation, 83:2 (2013)‎ 269-277.## 2. Montgomery D. C., Peck E. A., "Introduction to linear regression analysis", 2nd Edition, New York: Wiley (1992). ## 3. Belsley D.A., Kuh E., Welsch R.E., "Regression Diagnostics: Identifying Influential Data and Sources of Collinear it", New York: John Wiley & Sons (1980). ## 4. Beckman R. J., Cook R. D., "Outliers", Techno metrics, 25 (2) (1983)119-149. ## 5. Barnett V., Lewis T., "Outliers in statistical data", New York: John Wiley & Sons (1984). ## 6. Abuzaid A. H., Hussin A. G., Mohamed I. B., "Identifying single outlier in linear circular regression model based on circular distance", Journal of Applied Probability and Statistics, 3 (1) (2008) 107-117. ## ‎7. Rambli A. B., Mohamed I., Abuzaid A. H., Hussin, A. G., "Identification of Influential Observations in Circular Regression Model", Proceedings of the Regional Conference on Statistical Sciences (RCSS’10) (2010) 195-203. ## 8. Downs T. D., Mardia K.V., "Circular regression", Biometrika, 89(3) (2002) 683-697. ## 9. Abuzaid A. H., Mohamed I. B., Hussin A. G., Rambli A., "Covratio statistic for simple circular regression model", Chiang Mai J. Sci., 38(3) (2011) 321-330. ## 10. Ibrahim S., Rambli A., Hussin A.G., Mohamed I., "Outlier detection in a circular regression model using COVRATIO statistic", Communications in Statistics-Simulation and Computation, 42 (10) (2013) 2272-2280. ## 11. Jammalamadaka S. R., Sarma Y. R., "Circular regression. In Statistical Sciences and Data Analysis", edited by Matusita, K. Utrecht: VSP. (1993) 109-128. ## 12. Rambli A., Yunus R. M., Mohamed I., Hussin A. G., "Outlier Detection in a Circular Regression Model", Sains Malaysiana, 44 (7) (2015) 1027-1032## 13. Gould A. L., "A regression technique for angular data", Biometrics,25 (1969) 683-700. ‎14. Johnson R. A., Wehrly T. E., "Some angular-linear distributions and related regression models", ‎‎Journal of the American Statistical Association, 73 (1987) 602-606. ## ‎15. Fisher ‎‎N‎. ‎I‎., Lee‎‎ A‎. ‎J‎., ‎"Regression models for an angular response"‎, Biometrics, 48‎‎ (1992)‎ 665-677. ## 16. Watson G. S., "Goodness-of-fit tests on the circle, Biometrics", 48 (1961)109-114. ##