Abstract:
Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of variables and a relatively small number of cases are common place in modern statistical applications. In these cases, global down-weighting of an entire case, as performed by traditional robust procedures, may lead to poor results. We highlight the need for a new generation of robust estimators that can efficiently deal with cellwise outliers and at the same time show good performance under casewise outliers. © 2015, Sociedad de Estadística e Investigación Operativa.
Registro:
Documento: |
Artículo
|
Título: | Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination |
Autor: | Agostinelli, C.; Leung, A.; Yohai, V.J.; Zamar, R.H. |
Filiación: | Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari di Venezia, San Giobbe, Cannaregio 873, Venezia, 30121, Italy Department of Statistics, University of British Columbia, 3182-2207 Main Mall, Vancouver, BC V6T 1Z4, Canada Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1426, Argentina
|
Palabras clave: | Cellwise contamination; Multivariate data analysis; Multivariate location and scatter; Robust estimation |
Año: | 2015
|
Volumen: | 24
|
Número: | 3
|
Página de inicio: | 441
|
Página de fin: | 461
|
DOI: |
http://dx.doi.org/10.1007/s11749-015-0450-6 |
Título revista: | Test
|
Título revista abreviado: | Test
|
ISSN: | 11330686
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v24_n3_p441_Agostinelli |
Referencias:
- Alqallaf, F., Van Aelst, S., Yohai, V.J., Zamar, R.H., Propagation of outliers in multivariate data (2009) Ann Stat, 37 (1), pp. 311-331
- Alqallaf, F.A., Konis, K.P., Martin, R.D., Zamar, R.H., Scalable robust covariance and correlation estimates for data mining (2002) Proceedings of the eighth ACM SIGKDD international conference on knowledge discovery and data mining, , KDD ’02, pp 14–23 10.1145/775047.775050
- Danilov, M., Robust estimation of multivariate scatter under non-affine equivarint scenarios. Dissertation (2010) University of British Columbia
- Danilov, M., Yohai, V.J., Zamar, R.H., Robust estimation of multivariate location and scatter in the presence of missing data (2012) J Am Stat Assoc, 107, pp. 1178-1186
- Davies, P., Asymptotic behaviour of S-estimators of multivariate location parameters and dispersion matrices (1987) Ann Stat, 15, pp. 1269-1292
- Donoho, D.L., (1982) Breakdown properties of multivariate location estimators, , Dissertation: Harvard University
- Farcomeni, A., Robust constrained clustering in presence of entry-wise outliers (2014) Technometrics, 56, pp. 102-111
- Gervini, D., Yohai, V.J., A class of robust and fully efficient regression estimators (2002) Ann Stat, 30 (2), pp. 583-616
- Huber, P.J., Ronchetti, E.M., (1981) Robust statistics, , Wiley, New Jersey
- Hubert, M., Rousseeuw, P.J., Vakili, K., Shape bias of robust covariance estimators: an empirical study (2014) Stat Pap, 55, pp. 15-28
- Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust statistic: theory and methods, , Wiley, Chichister
- Rousseeuw, P.J., Multivariate estimation with high breakdown point (1985) Grossmann W, Pflug G, Vincze I, Wertz W, pp. 256-272. , Reidel Publishing Company, Dordrecht
- Rousseeuw, P.J., Van Driessen, K., A fast algorithm for the minimum covariance determinant estimator (1999) Technometrics, 41, pp. 212-223
- Salibian-Barrera, M., Yohai, V.J., A fast algorithm for S-regression estimates (2006) J Comput Gr Stat, 15 (2), pp. 414-427
- Smith, R.E., Campbell, N.A., Licheld, A., Multivariate statistical techniques applied to pisolitic laterite geochemistry at Golden Grove, Western Australia (1984) J Geochem Explor, 22, pp. 193-216
- Stahel, W.A., Breakdown of covariance estimators. Tech. Rep. 31 (1981) Fachgruppe für Statistik, , ETH Zürich, Switzerland
- Stahel, W.A., Maechler, M., Comment on “invariant co-ordinate selection (2009) J R Stat Soc Ser B Stat Methodol, 71, pp. 584-586
- Tatsuoka, K.S., Tyler, D.E., On the uniqueness of S-functionals and M-functionals under nonelliptical distributions (2000) Ann Stat, 28, pp. 1219-1243
- Van Aelst, S., Vandervieren, E., Willems, G., A Stahel–Donoho estimator based on huberized outlyingness (2012) Comput Stat Data Anal, 56, pp. 531-542
- Yohai, V.J., High breakdown point and high efficiency robust estimates for regression. Tech. Rep. 66, Department of Statistics, University of Washington (1985) Available:, , http://www.stat.washington.edu/research/reports/1985/tr066.pdf
Citas:
---------- APA ----------
Agostinelli, C., Leung, A., Yohai, V.J. & Zamar, R.H.
(2015)
. Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination. Test, 24(3), 441-461.
http://dx.doi.org/10.1007/s11749-015-0450-6---------- CHICAGO ----------
Agostinelli, C., Leung, A., Yohai, V.J., Zamar, R.H.
"Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination"
. Test 24, no. 3
(2015) : 441-461.
http://dx.doi.org/10.1007/s11749-015-0450-6---------- MLA ----------
Agostinelli, C., Leung, A., Yohai, V.J., Zamar, R.H.
"Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination"
. Test, vol. 24, no. 3, 2015, pp. 441-461.
http://dx.doi.org/10.1007/s11749-015-0450-6---------- VANCOUVER ----------
Agostinelli, C., Leung, A., Yohai, V.J., Zamar, R.H. Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination. Test. 2015;24(3):441-461.
http://dx.doi.org/10.1007/s11749-015-0450-6