Robust estimation of multivariate location and scatter in the presence of missing data

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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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Autor principal: Danilov, M.
Otros Autores: Yohai, V.J, Zamar, R.H
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2012
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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100 1 |a Danilov, M. 
245 1 0 |a Robust estimation of multivariate location and scatter in the presence of missing data 
260 |c 2012 
270 1 0 |m Danilov, M.; Quantitative Analyst at Google, 1600 Amphitheatre Parkway, Mountain View, CA 94043, United States; email: mikedanilov@google.com 
506 |2 openaire  |e Política editorial 
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504 |a Croux, C., Filzmoser, P., Joossens, K., Classification Efficiencies for Robust Discriminant Analysis (2008) Statistica Sinica, 18, pp. 588-599. , [1178] 
504 |a Danilov, M., (2010) Robust Estimation Or Multivariate Scatter Under Non- Affine Equivariant Scenarios, , Ph.D. dissertation, Department of Statistics, University of British Columbia. [1182] 
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504 |a Harrison, D., Rubinfeld, D.L., Hedonic Housing Prices and the Demand for Clean Air (1978) Journal of Environmental Economics and Management, 5, pp. 81-102. , [1184] 
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504 |a Little, R.J.A., Rubin, D.B., (2002) Statistical Analysis With Missing Data, , 2nd ed.), New York: Wiley, [1178,1182] 
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504 |a Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust Statistics: Theory and Methods, , Chichister: Wiley, [1178,1182,1184] 
504 |a Rocke, D.M., Robustness Properties of S-Estimators of Multivariate Location and Shape in High Dimension (1996) The Annals of Statistics, 24, pp. 1327-1345. , [1178] 
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504 |a Rousseeuw, P.J., van Driessen, K., A Fast Algorithm for the MinimumCovariance Determinant Estimator (1999) Technometrics, 41, pp. 212-223. , [1178] 
504 |a Salibian-Barrera, M., van Aelst, S., Willems, G., PCA Based on Multivariate MM-Estimators With Fast and Robust Bootstrap (2006) Journal of the American Statistical Association, 101, pp. 1198-1211. , [1178,1181] 
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504 |a Taskinen, S., Croux, C., Kankainen, A., Ollila, E., Oja, H., Influence Functions and Efficiencies of the Canonical Correlation and Vector Estimates Based on Scatter and Shape Matrices (2006) Journal of Multivariate Analysis, 97, pp. 359-384. , [1178,1181] 
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520 3 |a 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.  |l eng 
536 |a Detalles de la financiación: Natural Sciences and Engineering Research Council of Canada 
536 |a Detalles de la financiación: Universidad de Buenos Aires, PIP 5505 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PICT 00899 
536 |a Detalles de la financiación: Mike Danilov is a Quantitative Analyst at Google, 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA (E-mail: mikedanilov@google.com), Víctor J. Yohai is Emeritus Professor, Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Univer-sitaria, Pabellón 1, 1428 Buenos Aires, Argentina (E-mail: vyohai@dm.uba.ar), and Ruben H. Zamar is Professor, Department of Statistics, University of British Columbia, 333-6356 Agricultural Road, Vancouver, BC V6T 1Z2, Canada (E-mail: ruben@stat.ubc.ca). This research was partially supported by grants X-018 and X-447 from the University of Buenos Aires, PIP 5505 from CONICET, PICT 00899 from ANPCyT, and Discovery grant from NSERC. We thank the Associate Editor and two referees for their comments and suggestions which resulted in several important improvements on the first version of this article. 
593 |a Quantitative Analyst at Google, 1600 Amphitheatre Parkway, Mountain View, CA 94043, United States 
593 |a Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina 
593 |a Department of Statistics, University of British Columbia, 333-6356 Agricultural Road, Vancouver, BC V6T 1Z2, Canada 
690 1 0 |a CONSISTENT 
690 1 0 |a ELLIPTICAL DISTRIBUTION 
690 1 0 |a EM ALGORITHM 
690 1 0 |a FIXED POINT EQUATION 
700 1 |a Yohai, V.J. 
700 1 |a Zamar, R.H. 
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