Multivariate location and scatter matrix estimation under cellwise and casewise contamination

• Autores: Leung, Andy; Yohai, Victor Jaime; Zamar, Ruben Horacio
• Año de publicación: 2017
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Cellwise Outliers; Componentwise Contamination; Multivariate Location And Scatter; Robust Estimation
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Leung, Andy. University of British Columbia; Canadá
Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Zamar, Ruben Horacio. University of British Columbia; Canadá