Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter

Andrea Cerioli, Alessio Farcomeni and Marco Riani

Journal of Multivariate Analysis, 2014, vol. 126, issue C, 167-183

Abstract: The Forward Search is a powerful general method for detecting anomalies in structured data, whose diagnostic power has been shown in many statistical contexts. However, despite the wealth of empirical evidence in favor of the method, only few theoretical properties have been established regarding the resulting estimators. We show that the Forward Search estimators are strongly consistent at the multivariate normal model. We also obtain their finite sample breakdown point. Our results put the Forward Search approach for multivariate data on a solid statistical ground, which formally motivates its use in robust applied statistics. Furthermore, they allow us to compare the Forward Search estimators with other well known multivariate high-breakdown techniques.

Keywords: Elliptical truncation; Forward Search; Generalized Mahalanobis distances; High-breakdown estimation; Multivariate trimming; Robust diagnostics (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (18)

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DOI: 10.1016/j.jmva.2013.12.010

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