AN OUTLIER DETECTION METHOD FOR CIRCULAR LINEAR FUNCTIONAL RELATIONSHIP MODEL USING COVRATIO STATISTICS
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Published:
Sep 30, 2019
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Abstract
The existence of outlier may affect data aberrantly. However, outlier detection problem has been frequently discussed for linear data but limited on circular data. Thus, this paper discusses an outlier detection method on circular data. We focus on circular data with equal error concentration parameters where the data is studied using linear functional relationship model. In this paper, the data and the error terms are distributed with von Mises distribution. We modify the covratio statistics in which the correction factor is applied to the estimation of concentration parameter. We develop the cut-off equation based on the 5% upper percentile of the covratio statistics and the power of performance of outlier detection is examined by a Monte Carlo simulation study. The simulation result shows that the power of performance increases when the concentration and the level of contamination increase. The applicability of the proposed method is illustrated by using the wind direction data collected from the Holderness Coastline at the Humberside Coast in North Sea, United Kingdom.
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Mokhtar, N. A., Zubairi, Y. Z., Hussin, A. G., & Moslim, N. H. (2019). AN OUTLIER DETECTION METHOD FOR CIRCULAR LINEAR FUNCTIONAL RELATIONSHIP MODEL USING COVRATIO STATISTICS. Malaysian Journal of Science, 38(Sp2), 46–54. https://doi.org/10.22452/mjs.sp2019no2.5
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ISMI-ICTAS18 (Published)
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References
Abuzaid, A., Mohamed I, Hussin, A. G. and Rambli, A. (2011). Covratio statistics for simple circular regression model. Chiang Mai Journal of Science, 2011. 38 (3): 321-330.
Belsley, D. A., Kuh, E and Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley.
Caires, S. and Wyatt, L. R. (2003). A linear functional relationship model for circular data with an application to the assessment of ocean wave
measurement. Journal of Agricultural, Biological, and Environmental Statistics, Biological and Environmental Statistics, 8 (2): 153-169.
Dobson, A. (1978). Simple approximations for the Von Mises concentration statistic. Journal of the Royal Statistical Society. Series C (Applied Statistics), 27(3): 345-347.
Duan, L., Xu, L., Liu, Y. and Lee, J. (2009). Cluster-based outlier detection. Annals of Operations Research, 168(1): 151-168.
Fisher, N. I. (1993). Statistical Analysis of Circular Data. United Kingdom: Cambridge University Press.
Ghapor, A. A, Zubairi, Y. Z, Mamun, A. S. M. A. and Imon, A. H. M. R. (2014). On detecting outlier in simple linear functional relationship model using covratio statistic. Pakistan Journal of Statistics, 30(1): 129-142.
Hassan, S. F, Hussin, A. G. and Zubairi, Y. Z. (2010). Estimation of functional relationship model for circular variables and its application in measurement problem. Chiang Mai Journal of Science, 37(2): 195-205.
Hussin, A. G., Fieller, N. R. J. and Stillman, E. C. (2004). Linear regression for circular variables with application to directional data. Journal of Applied
Science & Technology, 8(1 & 2): 1-6.
Hussin, A.G., Abuzaid, A.H., Ibrahim, A.I.N. & Rambli, A. (2013). Detection of outliers in the complex linear regression model. Sains Malaysiana, 42(6): 869–874
Ibrahim S, Rambli A, Hussin A G and Mohamed I. (2013). Outlier detection in a circular regression model using covratio statistic. Communication in Statistics-Simulation and Computation, 42(10): 2272-2280.
Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics. New Jersey: John Wiley & Sons.
Mokhtar, N. A., Zubairi, Y. Z. and Hussin, A. G. (2015). A simple linear functional relationship model for circular variables and its application. Proceedings of the 9th International Conference on Renewable Energy Sources (RES '15), Kuala Lumpur, Malaysia, pp. 57-63.
Mokhtar, N. A., Zubairi, Y. Z., & Hussin, A. G. (2018). A clustering approach to detect multiple outliers in linear functional relationship model for circular data. Journal of Applied Statistics, 45(6): 1041-1051.
Rambli, A., Abuzaid, A. H. M. , Mohamed, I. B. and Hussin, A. G. (2016). Procedure for detecting outliers in a circular regression model. PLOS ONE, 11(4): e0153074.
Belsley, D. A., Kuh, E and Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley.
Caires, S. and Wyatt, L. R. (2003). A linear functional relationship model for circular data with an application to the assessment of ocean wave
measurement. Journal of Agricultural, Biological, and Environmental Statistics, Biological and Environmental Statistics, 8 (2): 153-169.
Dobson, A. (1978). Simple approximations for the Von Mises concentration statistic. Journal of the Royal Statistical Society. Series C (Applied Statistics), 27(3): 345-347.
Duan, L., Xu, L., Liu, Y. and Lee, J. (2009). Cluster-based outlier detection. Annals of Operations Research, 168(1): 151-168.
Fisher, N. I. (1993). Statistical Analysis of Circular Data. United Kingdom: Cambridge University Press.
Ghapor, A. A, Zubairi, Y. Z, Mamun, A. S. M. A. and Imon, A. H. M. R. (2014). On detecting outlier in simple linear functional relationship model using covratio statistic. Pakistan Journal of Statistics, 30(1): 129-142.
Hassan, S. F, Hussin, A. G. and Zubairi, Y. Z. (2010). Estimation of functional relationship model for circular variables and its application in measurement problem. Chiang Mai Journal of Science, 37(2): 195-205.
Hussin, A. G., Fieller, N. R. J. and Stillman, E. C. (2004). Linear regression for circular variables with application to directional data. Journal of Applied
Science & Technology, 8(1 & 2): 1-6.
Hussin, A.G., Abuzaid, A.H., Ibrahim, A.I.N. & Rambli, A. (2013). Detection of outliers in the complex linear regression model. Sains Malaysiana, 42(6): 869–874
Ibrahim S, Rambli A, Hussin A G and Mohamed I. (2013). Outlier detection in a circular regression model using covratio statistic. Communication in Statistics-Simulation and Computation, 42(10): 2272-2280.
Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics. New Jersey: John Wiley & Sons.
Mokhtar, N. A., Zubairi, Y. Z. and Hussin, A. G. (2015). A simple linear functional relationship model for circular variables and its application. Proceedings of the 9th International Conference on Renewable Energy Sources (RES '15), Kuala Lumpur, Malaysia, pp. 57-63.
Mokhtar, N. A., Zubairi, Y. Z., & Hussin, A. G. (2018). A clustering approach to detect multiple outliers in linear functional relationship model for circular data. Journal of Applied Statistics, 45(6): 1041-1051.
Rambli, A., Abuzaid, A. H. M. , Mohamed, I. B. and Hussin, A. G. (2016). Procedure for detecting outliers in a circular regression model. PLOS ONE, 11(4): e0153074.