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Abstract:

Real data may contain both cellwise outliers and casewise outliers. There is a vast literature on robust estimation for casewise outliers, but only a scant literature for cellwise outliers and almost none for both types of outliers. Estimation of multivariate location and scatter matrix is a corner stone in multivariate data analysis. A two-step approach was recently proposed to perform robust estimation of multivariate location and scatter matrix in the presence of cellwise and casewise outliers. In the first step a univariate filter was applied to remove cellwise outliers. In the second step a generalized S-estimator was used to downweight casewise outliers. This proposal can be further improved in three main directions. First, through the introduction of a consistent bivariate filter to be used in combination with the univariate filter in the first step. Second, through the proposal of a new fast subsampling procedure to generate starting points for the generalized S-estimator in the second step. Third, through the use of a non-monotonic weight function for the generalized S-estimator to better handle casewise outliers in high dimension. A simulation study and a real data example show that, unlike the original two-step procedure, the modified two-step approach performs and scales well in high dimension. Moreover, they show that the modified procedure outperforms the original one and other state-of-the-art robust procedures under cellwise and casewise data contamination. © 2017 Elsevier B.V.

Registro:

Documento: Artículo
Título:Multivariate location and scatter matrix estimation under cellwise and casewise contamination
Autor:Leung, A.; Yohai, V.; Zamar, R.
Filiación:Department of Statistics, University of British Columbia, 3182-2207 Main Mall, Vancouver, British Columbia, V6T 1Z4, Canada
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1426, Argentina
Palabras clave:Cellwise outliers; Componentwise contamination; Multivariate location and scatter; Robust estimation; Location; Matrix algebra; Multivariant analysis; Cellwise outliers; Componentwise; Multivariate data analysis; Robust estimation; Robust procedures; Simulation studies; Two-step approach; Two-step procedure; Statistics
Año:2017
Volumen:111
Página de inicio:59
Página de fin:76
DOI: http://dx.doi.org/10.1016/j.csda.2017.02.007
Título revista:Computational Statistics and Data Analysis
Título revista abreviado:Comput. Stat. Data Anal.
ISSN:01679473
CODEN:CSDAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v111_n_p59_Leung

Referencias:

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Citas:

---------- APA ----------
Leung, A., Yohai, V. & Zamar, R. (2017) . Multivariate location and scatter matrix estimation under cellwise and casewise contamination. Computational Statistics and Data Analysis, 111, 59-76.
http://dx.doi.org/10.1016/j.csda.2017.02.007
---------- CHICAGO ----------
Leung, A., Yohai, V., Zamar, R. "Multivariate location and scatter matrix estimation under cellwise and casewise contamination" . Computational Statistics and Data Analysis 111 (2017) : 59-76.
http://dx.doi.org/10.1016/j.csda.2017.02.007
---------- MLA ----------
Leung, A., Yohai, V., Zamar, R. "Multivariate location and scatter matrix estimation under cellwise and casewise contamination" . Computational Statistics and Data Analysis, vol. 111, 2017, pp. 59-76.
http://dx.doi.org/10.1016/j.csda.2017.02.007
---------- VANCOUVER ----------
Leung, A., Yohai, V., Zamar, R. Multivariate location and scatter matrix estimation under cellwise and casewise contamination. Comput. Stat. Data Anal. 2017;111:59-76.
http://dx.doi.org/10.1016/j.csda.2017.02.007