The change-of-variance function of M-estimators of scale under general contamination

Marc G. Genton; Peter J. Rousseeuw

doi:10.1016/0377-0427(95)00007-0

The change-of-variance function of M-estimators of scale under general contamination

Marc G. Genton, Peter J. Rousseeuw^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper we derive the change-of-variance function of M-estimators of scale under general contamination, thereby extending the formula in Hampel et al. (1986). We say that an M-estimator is B-robust if its influence function is bounded, and we call it V-robust if its change-of-variance function is bounded from above. It is shown, for a natural class of M-estimators, that the general notion of V-robustness still implies B-robustness. Several classes of M-estimators are studied closely, as well as some typical examples and their interpretation.

Original language	English (US)
Pages (from-to)	69-80
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	64
Issue number	1-2
DOIs	https://doi.org/10.1016/0377-0427(95)00007-0
State	Published - Nov 30 1995
Externally published	Yes

Keywords

B-robustness
Change-of-variance function
Influence function
V-robustness

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/0377-0427(95)00007-0

Cite this

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abstract = "In this paper we derive the change-of-variance function of M-estimators of scale under general contamination, thereby extending the formula in Hampel et al. (1986). We say that an M-estimator is B-robust if its influence function is bounded, and we call it V-robust if its change-of-variance function is bounded from above. It is shown, for a natural class of M-estimators, that the general notion of V-robustness still implies B-robustness. Several classes of M-estimators are studied closely, as well as some typical examples and their interpretation.",

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T1 - The change-of-variance function of M-estimators of scale under general contamination

AU - Genton, Marc G.

AU - Rousseeuw, Peter J.

PY - 1995/11/30

Y1 - 1995/11/30

N2 - In this paper we derive the change-of-variance function of M-estimators of scale under general contamination, thereby extending the formula in Hampel et al. (1986). We say that an M-estimator is B-robust if its influence function is bounded, and we call it V-robust if its change-of-variance function is bounded from above. It is shown, for a natural class of M-estimators, that the general notion of V-robustness still implies B-robustness. Several classes of M-estimators are studied closely, as well as some typical examples and their interpretation.

AB - In this paper we derive the change-of-variance function of M-estimators of scale under general contamination, thereby extending the formula in Hampel et al. (1986). We say that an M-estimator is B-robust if its influence function is bounded, and we call it V-robust if its change-of-variance function is bounded from above. It is shown, for a natural class of M-estimators, that the general notion of V-robustness still implies B-robustness. Several classes of M-estimators are studied closely, as well as some typical examples and their interpretation.

KW - B-robustness

KW - Change-of-variance function

KW - Influence function

KW - V-robustness

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U2 - 10.1016/0377-0427(95)00007-0

DO - 10.1016/0377-0427(95)00007-0

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AN - SCOPUS:0001956586

SN - 0377-0427

VL - 64

SP - 69

EP - 80

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

The change-of-variance function of M-estimators of scale under general contamination

Abstract

Keywords

ASJC Scopus subject areas

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