2016/09/01 by Leung, Andy, Yohai, Victor J., Zamar, Ruben H. · 1 citation
#62G05 #62G20 #62G35 #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1609.00402
We consider the problem of multivariate location and scatter matrix estimation when the data contain cellwise and casewise outliers. Agostinelli et al. (2015) propose a two-step approach to deal with this problem: first, apply a univariate filter to remove cellwise outliers and second, apply a generalized S-estimator to downweight casewise outliers. We improve this proposal in three main directions. First, we introduce a consistent bivariate filter to be used in combination with the univariate filter in the first step. Second, we propose a new fast subsampling procedure to generate starting points for the generalized S-estimator in the second step. Third, we consider a non-monotonic weight function for the generalized S-estimator to better deal with casewise outliers in high dimension. A simulation study and real data example show that, unlike the original two-step procedure, the modified two-step approach performs and scales well for high dimension. Moreover, the modified procedure outperforms the original one and other state-of-the-art robust procedures under cellwise and casewise data contamination.