Multivariate descriptive measures for location and scatter are the foundation of multivariate statistics and underpin many methods in the field. In this paper, we propose and study some new general depth-based trimmed means and trimmed scatter matrices. In addition to the basic properties and algorithms, we establish the asymptotic distributions of their sample versions. Using the asymptotic distributions, we study the asymptotic efficiencies of the sample trimmed means and the sample trimmed scatter matrices. Robustness is explored through finite-sample breakdown point. The results show that the sample trimmed means and trimmed scatter matrices are not only highly efficient but also exceptionally robust, making them very favorable estimators for multivariate location and scatter.
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