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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:126

Article

Cerioli, Andrea¹  Farcomeni, Alessio²  Riani, Marco¹ 

[1] Univ Parma, I-43100 Parma, Italy

[2] Univ Roma La Sapienza, I-00186 Rome, Italy

关键词: Elliptical truncation;    Forward Search;    Generalized Mahalanobis distances;    High-breakdown estimation;    Multivariate trimming;    Robust diagnostics;   

DOI  :  10.1016/j.jmva.2013.12.010

来源: Elsevier

【 摘 要 】

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 proper. ties 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free