Some Methods for Detecting Outliers
DOI:
https://doi.org/10.29304/jqcm.2022.14.4.1196Keywords:
Outliers, OutlierAbstract
Analyzing data need detecting some outliers; therefore many important methods appeared and introduced to detect these outliers. In this paper, we consider the distinguished methods employed to detect the outliers. Our main purpose, shed light the classical methods for detecting outliers and fixing disadvantage of these methods.
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References
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[31] Rainer D., Pavlo M.. (2016). Exact computation of the halfspace depth, Computational Statistics & Data Analysis, Volume 98, PP. 19-30, ISSN 0167-9473, https://doi.org/10.1016/j.csda.2015.12.011.
[32] Regina Y. Liu (1990). "On a Notion of Data Depth Based on Random Simplices," The Annals of Statistics, Ann. Statist. 18(1), 405-414.
[33] Robson, G. (2003). “Multiple outlier detection and cluster analysis of multivariate normal data.”.
[34] Rousseeuw, P. & Ruts, I. (1996). Algorithm AS 307: Bivariate Location Depth. Journal of the Royal Statistical Society Series C Applied Statistics. 45. 516-526. 10.2307/2986073.
[35] Rousseeuw, P. & Hubert, M. (1999). Regression Depth. Journal of the American Statistical Association. 94. 388-402. 10.1080/01621459.1999.10474129.
[36] Serfling, R. (2002). A Depth Function and a Scale Curve Based on Spatial Quantiles.
[37] Struyf, A. & Rousseeuw, P. (1999). Halfspace Depth and Regression Depth Characterize the Empirical Distribution. Journal of Multivariate Analysis. 69. 135-153. 10.1006/jmva.1998.1804.
[2] Baghfalaki, T. & Ganjali, M. (2017). Robust Weighted Generalized Estimating Equations Based on Statistical Depth. Communications in Statistics - Simulation and Computation. 46. 10.1080/03610918.2016.1277746.
[3] Berrendero, J.R. & Justel, A. & Svarc, M. (2011). Principal components for multivariate functional data. Computational Statistics & Data Analysis. 55. 2619-2634. 10.1016/j.csda.2011.03.011.
[4] Bremner, D. & Fukuda, K. & Rosta, V. (2006). Primal-dual algorithms for data depth. 10.1090/dimacs/072/12.
[5] Bremner, D. & Chen, D. & Iacono, J. & Langerman, S. & Morin, P. (2008). Output-sensitive algorithms for Tukey depth and related problems. Statistics and Computing. 18. 259-266. 10.1007/s11222-008-9054-2.
[6] Burr, M. & Rafalin, E. & Souvaine, D. (2011). Dynamic Maintenance of Half-Space Depth for Points and Contours.
[7] Cabana, E., Lillo, R.E. & Laniado, H. (2021). Multivariate outlier detection based on a robust Mahalanobis distance with shrinkage estimators. Stat Papers 62, 1583–1609. https://doi.org/10.1007/s00362-019-01148-1
[8] Cansiz S., “Mahalanobis Distance and Multivariate Outlier Detection in r.”2020.
[9] Y. Chen, X. Dang, H. Peng and H. L. Bart, “Outlier detection with the Kernelized spatial depth function,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 31, pp. 288–305, Feb. 2009.
[10] F. Dikbas, “Multivariate Outlier Detection by Using Two-Dimensional Correlation“ , CC BY 4.0 License, 2021.
[11] Donoho, D. & Gasko, M. (1992). Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness. Ann. Stat.. 20. 10.1214/aos/1176348890.
[12] Dutta, S. & Genton, M. (2017). Depth-weighted robust multivariate regression with application to sparse data. Canadian Journal of Statistics. 45. 10.1002/cjs.11315.
[13] Evans K, Love T, Thurston SW. (2015). “Outlier Identification in Model-Based Cluster Analysis”. J Classif. 32(1):63-84. doi: 10.1007/s00357-015-9171-5.
[14] Febrero M., Galeano P. and Gonz ́alez-Manteiga W., “Outlier detection in functional data by depth measures, withapplication to identify abnormal NOx levels “Wiley InterScience, Environmetrics ,19(4):331-345, 2007.
[15] Ghorbani H. , “ MAHALANOBIS DISTANCE AND ITS APPLICATION FOR DETECTING MULTIVARIATE OUTLIERS “, Ser. Math. Inform. Vol. 34, No 3 (2019), 583–595 .
[16] González-De La Fuente, L., Nieto-Reyes, A., Terán, P. (2022). Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth. Mathematics, 10, 2758. https://doi.org/10.3390/ math10152758.
[17] Hallin, M. & Paindaveine, D. & Siman, M. (2010). Multivariate Quantiles and Multiple-Output Regression Quantiles: From L1 Optimization to Halfspace Depth. The Annals of Statistics. 38. 635-669. 10.1214/09-AOS723.
[18] Harsh, A., Ball JE, Wei P. (2018). “Onion-Peeling Outlier Detection in 2-D data Sets.”, International Journal of Computer Applications, 139(3)pp. 26-31.
[19] M. Hubert, P. Rousseeuw and P. Segaert: Multivariate functional outlier detection. Statistical Methods & Applications. 24, PP. 237–243, (2015)
10.1007/s10260-015-0319-6.
[20] Hubert, M. & Rousseeuw, P. & Segaert, P. (2017). Multivariate and functional classification using depth and distance. Advances in Data Analysis and Classification. 11. 445–466. 10.1007/s11634-016-0269-3.
[21] R. Hyndman and H. Lin Shang,”Bagplots, Boxplots and Outlier Detection for Functional Data”. Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD, 2008.
[22] Ieva, F. & Tarabelloni, N. & Paganoni, A. & Biasi, R. (2015). Use of Depth Measure for Multivariate Functional Data in Disease Prediction: An Application to Electrocardiograph Signals. The International Journal of Biostatistics. 11. 10.1515/ijb-2014-0041.
[23] Johnson, T., Kwok, I., and Ng, R. (1998). Fast computation of 2- dimensional depth contours. In: Agrawal, R., and Stolorz, P. (eds.), Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining, AAAI Press, New York, 224–228.
[24] Kong, L. & Mizera, I., Quantile tomography: Using quantiles with multivariate data. Statistica Sinica. Vol. 22, No. 4 (October 2012), pp. 1589-1610. 10.5705/ss.2010.224.
[25] Liu, X. & Zuo, Y. (2014). Computing Halfspace Depth and Regression Depth. Communications in Statistics: Simulation and Computation. 43. 10.1080/03610918.2012.720744.
[26] Lok, W. S. & Lee S. M. (2011) A new statistical depth function with applications to multimodal data, Journal of Nonparametric Statistics, 23:3, 617-631, DOI: 10.1080/10485252.2011.553953.
[27] Lopez-Pintado, S. & Sun, Y. & Lin, J. & Genton, M. (2014). Simplicial band depth for multivariate functional data. Advances in Data Analysis and Classification. 8. 321-338. 10.1007/s11634-014-0166-6.
[28] Makinde, O. S. & Adewumi, A. D. (2017). A comparison of depth functions in maximal depth classification rules. Journal of Modern Applied Statistical Methods, 16(1), 388-405. doi: 10.22237/jmasm/1493598120.
[29] Miller, K. & Ramaswami, S. & Rousseeuw, P. & Sellarès, J. & Souvaine, D. & Streinu, I. & Struyf, A. (2003). Efficient computation of location depth contours by methods of computational geometry. Statistics and Computing. 13. 153-162. 10.1023/A:1023208625954.
[30] Mosler, K., Lange, T., and Bazovkin, P. (2009), “Computing zonoid trimmed regions of dimension d > 2”, Computational Statistics and Data Analysis 53, 2500-2510.
[31] Rainer D., Pavlo M.. (2016). Exact computation of the halfspace depth, Computational Statistics & Data Analysis, Volume 98, PP. 19-30, ISSN 0167-9473, https://doi.org/10.1016/j.csda.2015.12.011.
[32] Regina Y. Liu (1990). "On a Notion of Data Depth Based on Random Simplices," The Annals of Statistics, Ann. Statist. 18(1), 405-414.
[33] Robson, G. (2003). “Multiple outlier detection and cluster analysis of multivariate normal data.”.
[34] Rousseeuw, P. & Ruts, I. (1996). Algorithm AS 307: Bivariate Location Depth. Journal of the Royal Statistical Society Series C Applied Statistics. 45. 516-526. 10.2307/2986073.
[35] Rousseeuw, P. & Hubert, M. (1999). Regression Depth. Journal of the American Statistical Association. 94. 388-402. 10.1080/01621459.1999.10474129.
[36] Serfling, R. (2002). A Depth Function and a Scale Curve Based on Spatial Quantiles.
[37] Struyf, A. & Rousseeuw, P. (1999). Halfspace Depth and Regression Depth Characterize the Empirical Distribution. Journal of Multivariate Analysis. 69. 135-153. 10.1006/jmva.1998.1804.
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Published
2023-04-30
How to Cite
Habeeb, H. H. K. H. K., & Al-Guraibawi, M. (2023). Some Methods for Detecting Outliers. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(4), Stat. Page 28–36. https://doi.org/10.29304/jqcm.2022.14.4.1196
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Statistic Articles
