Robust estimation of multivariate location and scatter in the presence of missing data
Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and s...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_01621459_v107_n499_p1178_Danilov |
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todo:paper_01621459_v107_n499_p1178_Danilov2023-10-03T15:01:31Z Robust estimation of multivariate location and scatter in the presence of missing data Danilov, M. Yohai, V.J. Zamar, R.H. Consistent Elliptical distribution EM algorithm Fixed point equation Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S-estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random. We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online. © 2012 American Statistical Association. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01621459_v107_n499_p1178_Danilov |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Consistent Elliptical distribution EM algorithm Fixed point equation |
| spellingShingle |
Consistent Elliptical distribution EM algorithm Fixed point equation Danilov, M. Yohai, V.J. Zamar, R.H. Robust estimation of multivariate location and scatter in the presence of missing data |
| topic_facet |
Consistent Elliptical distribution EM algorithm Fixed point equation |
| description |
Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S-estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random. We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online. © 2012 American Statistical Association. |
| format |
JOUR |
| author |
Danilov, M. Yohai, V.J. Zamar, R.H. |
| author_facet |
Danilov, M. Yohai, V.J. Zamar, R.H. |
| author_sort |
Danilov, M. |
| title |
Robust estimation of multivariate location and scatter in the presence of missing data |
| title_short |
Robust estimation of multivariate location and scatter in the presence of missing data |
| title_full |
Robust estimation of multivariate location and scatter in the presence of missing data |
| title_fullStr |
Robust estimation of multivariate location and scatter in the presence of missing data |
| title_full_unstemmed |
Robust estimation of multivariate location and scatter in the presence of missing data |
| title_sort |
robust estimation of multivariate location and scatter in the presence of missing data |
| url |
http://hdl.handle.net/20.500.12110/paper_01621459_v107_n499_p1178_Danilov |
| work_keys_str_mv |
AT danilovm robustestimationofmultivariatelocationandscatterinthepresenceofmissingdata AT yohaivj robustestimationofmultivariatelocationandscatterinthepresenceofmissingdata AT zamarrh robustestimationofmultivariatelocationandscatterinthepresenceofmissingdata |
| _version_ |
1807321794916384768 |