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Robustness of the Affine Equivariant Scatter Estimator Based on the Spatial Rank Covariance Matrix

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  • Kai Yu
  • Xin Dang
  • Yixin Chen

Abstract

Visuri et al. (2000) proposed a technique for robust covariance matrix estimation based on different notions of multivariate sign and rank. Among them, the spatial rank based covariance matrix estimator that utilizes a robust scale estimator is especially appealing due to its high robustness, computational ease, and good efficiency. Also, it is orthogonally equivariant under any distribution and affinely equivariant under elliptically symmetric distributions. In this paper, we study robustness properties of the estimator with respective to two measures: breakdown point and influence function. More specifically, the upper bound of the finite sample breakdown point can be achieved by a proper choice of univariate robust scale estimator. The influence functions for eigenvalues and eigenvectors of the estimator are derived. They are found to be bounded under some assumptions. Moreover, finite sample efficiency comparisons to popular robust MCD, M, and S estimators are reported.

Suggested Citation

  • Kai Yu & Xin Dang & Yixin Chen, 2015. "Robustness of the Affine Equivariant Scatter Estimator Based on the Spatial Rank Covariance Matrix," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 914-932, March.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:5:p:914-932
    DOI: 10.1080/03610926.2012.755198
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    Cited by:

    1. Xin Dang & Hailin Sang & Lauren Weatherall, 2019. "Gini covariance matrix and its affine equivariant version," Statistical Papers, Springer, vol. 60(3), pages 641-666, June.

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