Projection based scatter depth functions and associated scatter estimators

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Zhou, Weihua¹  Dang, Xin² 

[1] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA

[2] Univ Mississippi, Dept Math, University, MS 38677 USA

关键词: Scatter depth function;    Scatter estimator;    Empirical depth process;    Limiting distribution;    Breakdown point;    Influence functions;    Efficiency;   

DOI  :  10.1016/j.jmva.2009.06.004

来源: Elsevier

【 摘 要 】

In this article, we study a class of projection based scatter depth functions proposed by Zuo [Y. Zuo, Robust location and scatter estimators in multivariate analysis, The Frontiers in Statistics, Imperial College Press, 2005. Invited book chapter to honor Peter Bickel on his 65th Birthday]. In order to use the depth function effectively, some favorable properties are suggested for the common scatter depth functions. We show that the proposed scatter depth totally satisfies these desirable properties and its sample version possess strong and root n uniform consistency. Under some regularity conditions, the limiting distribution of the empirical process of the scatter depth function is derived. We also found that the aforementioned depth functions assess the bounded influence functions. A maximum depth based affine equivariant scatter estimator is induced. The limiting distributions as well as the strong and root n consistency of the sample scatter estimators are established. The finite sample performance of the related scatter estimator shows that it has a very high breakdown point and good efficiency. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free