Keywords
Outliers
projection pursuit
kurtosis
Argentinian companies
projection pursuit
kurtosis
Argentinian companies
How to Cite
Stimolo, M. I., & Ortiz, P. A. (2020). Projection pursuit algorithms to detect outliers. Cuadernos De Administración, 33. https://doi.org/10.11144/Javeriana.cao33.ppado
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Abstract
In this paper, we compare the methods proposed by Peña and Prieto (2001), and Filzmoser, Maronna, and Werner (2008) to detect outliers in a set of Argentine companies that quote their shares in the Stock Exchange. A significant heterogeneity between observations can be a consequence of the presence of outliers. The detection of outliers is an important task for the statistical analysis since they distort descriptive measures and parameters estimators. There are different multivariate methods to detect outliers, such as distance-based methods and projection pursuit methods.
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Banker, R., & Byzalov, D. (2014). Asymmetric cost behavior. Journal of Management Accounting Research, 26(2), 43-79. https://doi.org/10.2308/jmar-50846
Bolsar (s.f). Buenos Aires Stock Exchange. https://www.bolsar.com/VistasDL/PaginaPrincipal.aspx
Campbell, N. A. (1980). Robust procedures in multivariate analysis I: Robust covariance estimation. Applied statistics, 231-237. https://doi.org/10.2307/2346896
Filzmoser, P. (2015). Gschwandtner M. mvoutlier: Multivariate outlier detection based on robust methods. R package version 2.0.6.In. Routine available at http://halweb.uc3m.es/esp/Personal/personas/fjp/research.htm
Filzmoser, P., Maronna, R., & Werner, M. (2008). Outlier identification in high dimensions. Computational Statistics & Data Analysis, 52(3), 1694-1711. https://doi.org/10.1016/j.csda.2007.05.018
Gnanadesikan, R., & Kettenring, J. (1972). Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics, 81-124. https://doi.org/10.2307/2528963
Maronna, R. A. (1976). Robust M-estimators of multivariate location and scatter. The Annals of Statistics, 51-67. https://doi.org/10.1214/aos/1176343347
Maronna, R. A., & Zamar, R. H. (2012). Robust estimates of location and dispersion for high-dimensional datasets. Technometrics. https://doi.org/10.1198/004017002188618509
Peña, D. (2002). Análisis de datos multivariantes, vol. 24. Madrid: McGraw-Hill.
Peña, D., & Prieto, F. J. (2001). Multivariate outlier detection and robust covariance matrix estimation. Technometrics, 43(3), 286-310. https://doi.org/10.1198/004017001316975899
Peña, D., & Yohai, V. (1999). A fast procedure for outlier diagnostics in large regression problems. Journal of the American Statistical Association, 94(446), 434-445. https://doi.org/10.1080/01621459.1999.10474138
Rocke, D. M. (1996). Robustness properties of S-estimators of multivariate location and shape in high dimension. The Annals of statistics, 1327-1345. https://doi.org/10.1214/aos/1032526972
Rousseeuw, P. J. (1985). Multivariate estimation with high breakdown point. Mathematical statistics and applications, 8, 283-297. https://www.researchgate.net/profile/Peter_Rousseeuw/publication/239666038_Multivariate_Estimation_With_High_Breakdown_Point/links/0deec53137b8cc68aa000000.pdf
Rousseeuw, P. J. (1993). A resampling design for computing high-breakdown regression. Statistics & probability letters, 18(2), 125-128. https://doi.org/10.1016/0167-7152(93)90180-Q
Rousseeuw, P. J., & Driessen, K. V. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41(3), 212-223. https://doi.org/10.1080/00401706.1999.10485670
Stahel, W. A. (1981). Robuste schätzungen: infinitesimale optimalität und schätzungen von kovarianzmatrizen: Eidgenössische Technische Hochschule - ETH. Zürich.
Uriel Jiménez, E., & Aldás Manzano, J. (2005). Análisis multivariante aplicado: aplicaciones al marketing, investigación de mercados, economía, dirección de empresas y turismo. Madrid: Thomson.
Banker, R., & Byzalov, D. (2014). Asymmetric cost behavior. Journal of Management Accounting Research, 26(2), 43-79. https://doi.org/10.2308/jmar-50846
Bolsar (s.f). Buenos Aires Stock Exchange. https://www.bolsar.com/VistasDL/PaginaPrincipal.aspx
Campbell, N. A. (1980). Robust procedures in multivariate analysis I: Robust covariance estimation. Applied statistics, 231-237. https://doi.org/10.2307/2346896
Filzmoser, P. (2015). Gschwandtner M. mvoutlier: Multivariate outlier detection based on robust methods. R package version 2.0.6.In. Routine available at http://halweb.uc3m.es/esp/Personal/personas/fjp/research.htm
Filzmoser, P., Maronna, R., & Werner, M. (2008). Outlier identification in high dimensions. Computational Statistics & Data Analysis, 52(3), 1694-1711. https://doi.org/10.1016/j.csda.2007.05.018
Gnanadesikan, R., & Kettenring, J. (1972). Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics, 81-124. https://doi.org/10.2307/2528963
Maronna, R. A. (1976). Robust M-estimators of multivariate location and scatter. The Annals of Statistics, 51-67. https://doi.org/10.1214/aos/1176343347
Maronna, R. A., & Zamar, R. H. (2012). Robust estimates of location and dispersion for high-dimensional datasets. Technometrics. https://doi.org/10.1198/004017002188618509
Peña, D. (2002). Análisis de datos multivariantes, vol. 24. Madrid: McGraw-Hill.
Peña, D., & Prieto, F. J. (2001). Multivariate outlier detection and robust covariance matrix estimation. Technometrics, 43(3), 286-310. https://doi.org/10.1198/004017001316975899
Peña, D., & Yohai, V. (1999). A fast procedure for outlier diagnostics in large regression problems. Journal of the American Statistical Association, 94(446), 434-445. https://doi.org/10.1080/01621459.1999.10474138
Rocke, D. M. (1996). Robustness properties of S-estimators of multivariate location and shape in high dimension. The Annals of statistics, 1327-1345. https://doi.org/10.1214/aos/1032526972
Rousseeuw, P. J. (1985). Multivariate estimation with high breakdown point. Mathematical statistics and applications, 8, 283-297. https://www.researchgate.net/profile/Peter_Rousseeuw/publication/239666038_Multivariate_Estimation_With_High_Breakdown_Point/links/0deec53137b8cc68aa000000.pdf
Rousseeuw, P. J. (1993). A resampling design for computing high-breakdown regression. Statistics & probability letters, 18(2), 125-128. https://doi.org/10.1016/0167-7152(93)90180-Q
Rousseeuw, P. J., & Driessen, K. V. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41(3), 212-223. https://doi.org/10.1080/00401706.1999.10485670
Stahel, W. A. (1981). Robuste schätzungen: infinitesimale optimalität und schätzungen von kovarianzmatrizen: Eidgenössische Technische Hochschule - ETH. Zürich.
Uriel Jiménez, E., & Aldás Manzano, J. (2005). Análisis multivariante aplicado: aplicaciones al marketing, investigación de mercados, economía, dirección de empresas y turismo. Madrid: Thomson.
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Copyright (c) 2020 Maria Inés Stimolo, Pablo Arnaldo Ortiz