The performance of Robust-Diagnostic F in the identification of multiple high leverage points
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| date | 2015-10-07 08:53:35 |
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| internalnotes | Bagheri, A., Habshah, M., & Imon, R. H. M. R. (2012). A novel collinearity-influential observation diagnostic measure based on a group deletion approach. Communications in Statistics: Simulation and Computation, 41(8), 1379-1396. doi:10.1080/03610918.2011.600497 Barnett, V., & Lewis, T. (1994). Outliers in Statistical Data, Retrieved from www.scopus.com Djauhari, M. A. (2010). A multivariate process variability monitoring based on individual observations. Modern Applied Science, 4(10), 91-96. Retrieved from www.scopus.com Fung, W. -. (1993). Unmasking outliers and leverage points: A confirmation. Journal of the American Statistical Association, 88(422), 515-519. doi:10.1080/01621459.1993.10476302 Habshah, M., Norazan, M. R., & Imon, A. H. M. R. (2009). The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression. Journal of Applied Statistics, 36(5), 507-520. doi:10.1080/02664760802553463 Hadi, A. S. (1992). Identifying multiple outliers in multivariate data. Journal of the Royal Statistical Society, 54(3), 761-771. Retrieved from www.scopus.com Hampel, F. (2001). Robust statistics: A brief introduction and overview. Robust Statistics: A Brief Introduction and Overview, Retrieved from www.scopus.com Hampel, F. R. (1971). A general qualitative definition of robustness. Ann.Math.Statist., 42, 1887-1896. Retrieved from www.scopus.com Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions, Retrieved from www.scopus.com Hardin, J., & Rocke, D. M. (2005). The distribution of robust distances. Journal of Computational and Graphical Statistics, 14(4), 928-946. doi:10.1198/106186005X77685 Hawkins, D. M., Bradu, D., & Kass, G. V. (1984). Location of several outliers in multiple-regression data using elemental sets. Technometrics, 26(3), 197-208. doi:10.1080/00401706.1984.10487956 Hodge, V. J., & Austin, J. (2004). A survey of outlier detection methodologies. Artificial Intelligence Review, 22(2), 85-126. doi:10.1023/B:AIRE.0000045502.10941.a9 Imon, A. H. M. R. (2002). Identifying multiple high leverage points in linear regression. Journal of Statistical Studies, 3, 207-218. Retrieved from www.scopus.com Maronna, R. A., Martin, R. D., & Yohai, V. J. (2006). Robust statistics: Theory and methods. Robust statistics: Theory and methods (pp. 1-403) doi:10.1002/0470010940 Retrieved from www.scopus.com Rahmatullah Imon, A. H. M. (2005). Identifying multiple influential observations in linear regression. Journal of Applied Statistics, 32(9), 929-946. doi:10.1080/02664760500163599 Rousseeuw, P. J., & Leroy, A. M. (1987). Robust Regression and Outlier Detection, Retrieved from www.scopus.com Rousseeuw, P. J., & van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association, 85(411), 633-639. doi:10.1080/01621459.1990.10474920 Salibian-Barrera, M., & Yohai, V. J. (2006). A fast algorithm for S-regression estimates. Journal of Computational and Graphical Statistics, 15(2), 414-427. doi:10.1198/106186006X113629 Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for regression. Ann.Statist., 15, 642-656. Retrieved from www.scopus.com |
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| spelling | 12386 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=12386 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal UniSZA Unisza unisza image/jpeg inches 96 96 35 35 1425 793 1425x793 2015-10-07 08:53:35 6686-01-FH02-FESP-15-03876.jpg UniSZA Private Access The performance of Robust-Diagnostic F in the identification of multiple high leverage points Pakistan Journal of Statistics High leverage points have undue effects on the Least Square estimates. They are responsible for misleading conclusions in regression and multicollinearity problems. Hence, it is imperative to detect high leverage points and use robust estimators to estimate the parameters of a regression model, so as to arrive at valid conclusions. Several well-known methods have failed to detect multiple high leverage points correctly because of the swamping and/or masking effects. The Diagnostic Robust Generalized Potential (DRGP), is an appealing alternative method that successfully detects high leverage points correctly. However, for small percentages of high leverage points, it has the tendency to identify few low leverage points to be points of high leverage. In this paper, an attempt is made to correctly identify real high leverage point by reducing swamping effects. We propose a method we call Robust Diagnostic-F (RDF), in which robust approach is employed to detect the suspected high leverage points. Then, F statistics that relates the change in data covariance structure is used to confirm the suspicion. The performance of RDF is evaluated through real data and simulations. Comparisons are also made with existing methods. 31 5 ISOSS Publications ISOSS Publications 461-472 Bagheri, A., Habshah, M., & Imon, R. H. M. R. (2012). A novel collinearity-influential observation diagnostic measure based on a group deletion approach. Communications in Statistics: Simulation and Computation, 41(8), 1379-1396. doi:10.1080/03610918.2011.600497 Barnett, V., & Lewis, T. (1994). Outliers in Statistical Data, Retrieved from www.scopus.com Djauhari, M. A. (2010). A multivariate process variability monitoring based on individual observations. Modern Applied Science, 4(10), 91-96. Retrieved from www.scopus.com Fung, W. -. (1993). Unmasking outliers and leverage points: A confirmation. Journal of the American Statistical Association, 88(422), 515-519. doi:10.1080/01621459.1993.10476302 Habshah, M., Norazan, M. R., & Imon, A. H. M. R. (2009). The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression. Journal of Applied Statistics, 36(5), 507-520. doi:10.1080/02664760802553463 Hadi, A. S. (1992). Identifying multiple outliers in multivariate data. Journal of the Royal Statistical Society, 54(3), 761-771. Retrieved from www.scopus.com Hampel, F. (2001). Robust statistics: A brief introduction and overview. Robust Statistics: A Brief Introduction and Overview, Retrieved from www.scopus.com Hampel, F. R. (1971). A general qualitative definition of robustness. Ann.Math.Statist., 42, 1887-1896. Retrieved from www.scopus.com Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions, Retrieved from www.scopus.com Hardin, J., & Rocke, D. M. (2005). The distribution of robust distances. Journal of Computational and Graphical Statistics, 14(4), 928-946. doi:10.1198/106186005X77685 Hawkins, D. M., Bradu, D., & Kass, G. V. (1984). Location of several outliers in multiple-regression data using elemental sets. Technometrics, 26(3), 197-208. doi:10.1080/00401706.1984.10487956 Hodge, V. J., & Austin, J. (2004). A survey of outlier detection methodologies. Artificial Intelligence Review, 22(2), 85-126. doi:10.1023/B:AIRE.0000045502.10941.a9 Imon, A. H. M. R. (2002). Identifying multiple high leverage points in linear regression. Journal of Statistical Studies, 3, 207-218. Retrieved from www.scopus.com Maronna, R. A., Martin, R. D., & Yohai, V. J. (2006). Robust statistics: Theory and methods. Robust statistics: Theory and methods (pp. 1-403) doi:10.1002/0470010940 Retrieved from www.scopus.com Rahmatullah Imon, A. H. M. (2005). Identifying multiple influential observations in linear regression. Journal of Applied Statistics, 32(9), 929-946. doi:10.1080/02664760500163599 Rousseeuw, P. J., & Leroy, A. M. (1987). Robust Regression and Outlier Detection, Retrieved from www.scopus.com Rousseeuw, P. J., & van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association, 85(411), 633-639. doi:10.1080/01621459.1990.10474920 Salibian-Barrera, M., & Yohai, V. J. (2006). A fast algorithm for S-regression estimates. Journal of Computational and Graphical Statistics, 15(2), 414-427. doi:10.1198/106186006X113629 Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for regression. Ann.Statist., 15, 642-656. Retrieved from www.scopus.com |
| spellingShingle | The performance of Robust-Diagnostic F in the identification of multiple high leverage points |
| summary | High leverage points have undue effects on the Least Square estimates. They are responsible for misleading conclusions in regression and multicollinearity problems. Hence, it is imperative to detect high leverage points and use robust estimators to estimate the parameters of a regression model, so as to arrive at valid conclusions. Several well-known methods have failed to detect multiple high leverage points correctly because of the swamping and/or masking effects. The Diagnostic Robust Generalized Potential (DRGP), is an appealing alternative method that successfully detects high leverage points correctly. However, for small percentages of high leverage points, it has the tendency to identify few low leverage points to be points of high leverage. In this paper, an attempt is made to correctly identify real high leverage point by reducing swamping effects. We propose a method we call Robust Diagnostic-F (RDF), in which robust approach is employed to detect the suspected high leverage points. Then, F statistics that relates the change in data covariance structure is used to confirm the suspicion. The performance of RDF is evaluated through real data and simulations. Comparisons are also made with existing methods. |
| title | The performance of Robust-Diagnostic F in the identification of multiple high leverage points |
| title_full | The performance of Robust-Diagnostic F in the identification of multiple high leverage points |
| title_fullStr | The performance of Robust-Diagnostic F in the identification of multiple high leverage points |
| title_full_unstemmed | The performance of Robust-Diagnostic F in the identification of multiple high leverage points |
| title_short | The performance of Robust-Diagnostic F in the identification of multiple high leverage points |
| title_sort | performance of robust-diagnostic f in the identification of multiple high leverage points |