Maxbias curves of robust location estimators based on subranges

[en] A maxbias curve is a powerful tool to describe the robustness of an estimator. It tells us how much an estimator can change due to a given fraction of contamination. In this paper, maxbias curves are computed for some univariate location estimators based on subranges: midranges, trimmed means and the univariate Minimum Volume Ellipsoid (MVE) location estimators. These estimators are intuitively appealing and easy to calculate.

Disciplines :

Mathematics

Author, co-author :

Croux, C.

Haesbroeck, Gentiane ; Université de Liège - ULiège > Département de mathématique > Statistique (aspects théoriques)

Language :

English

Title :

Maxbias curves of robust location estimators based on subranges

Publication date :

June 2002

Journal title :

Journal of Nonparametric Statistics

ISSN :

1048-5252

eISSN :

1029-0311

Publisher :

Taylor & Francis Ltd, Abingdon, United Kingdom

Volume :

Issue :

Pages :

295-306

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 23 September 2009

Statistics

Number of views

85 (4 by ULiège)

Number of downloads

1 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

publications

supporting

mentioning

contrasting

Smart Citations

Citing PublicationsSupportingMentioningContrasting

View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

Bibliography

Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H. and Tukey, J.W. (1972) Robust Estimation of Location: Survey and Advances. Princeton, NJ: Princeton University Press.
Berrendero, J.R. and Zamar, R.H. (1999) Global robustness of location and dispersion estimates, Statistics and Probability Letters, 44, 63-72.
Butler, R.W., Davies, P.L. and Jhun, M. (1993) Asymptotics for the minimum covariance determinant estimator, The Annals of Statistics, 21, 1385-1400.
Chen, Z. and Tyler, D.E. The influence function and maximum bias of Tukey's median, To appear in The Annals of Statistics.
Croux, C. (1996) Maximum deviation curves for location estimators, Statistics, 28, 285-305.
Croux, C. and Haesbroeck, G. (1999) Influence function and efficiency of the minimum covariance determinant scatter matrix estimator, Journal of Multivariate Analysis, 71, 161-190.
Croux, C. and Haesbroeck, G. (2001) Maxbias curves of robust scale estimators based on subranges, Metrika, 53, 101-122.
Croux, C., Haesbroeck, G. and Rousseeuw, P.S. Location Adjustment for the Minimum Volume Ellipsoid Estimator, To appear in Statistics and Computing.
Davies, P.L. (1993) Aspects of robust linear regression, The Annals of Statistics, 21, 1843-1899.
Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986) Robust Statistics: The Approach based on Influence Functions. New York: Wiley.
Huber, P.J. (1964) Robust estimation of a location parameter, The Annals of Mathematical Statistics, 35, 73-101.
Huber, P.J. (1981) Robust Statistics. New York: Wiley.
Martin, R.D., Zamar, R.H. (1993) Bias robust estimation of scale, The Annals of Statistics, 21, 1991-1017.
Oosterhoff, J. (1994) Trimmed mean or sample median? Statistics and Probability Letters, 20, 401-409.
Rousseeuw, P.J. (1985) Multivariate estimation with high breakdown point, In: Grossmann, W., Pflug, G., Vincze, I. and Wertz, W. (Eds.), Mathematical Statistics and Applications (Vol. B). Dordrecht: Reidel, pp. 283-297.
Rousseeuw, P.J. (1998) Maxbias curves, In: Kotz, S., Read, C. and Banks, D. (Eds.), Encyclopedia of Statistical Sciences (Update Vol. 3). New York: Wiley.
Rousseeuw, P.J. and Leroy, A.M. (1987) Robust Regression and Outlier Detection. New York: Wiley.
Yohai, V.J. and Maronna, R.A. (1990) The maximum bias of robust covariances, Comunications in Statistics Part A - Theory and Methods, 19, 3925-3933.

Similar publications

Sorry the service is unavailable at the moment. Please try again later.

Name	Provider / Domaine	Expiration	Description
JSESSIONID	Oracle Corporation www.uliege.be	Session	General purpose platform session cookie, used by sites written in JSP. Usually used to maintain an anonymous user session by the server.
CookieScriptConsent	CookieScript .uliege.be	1 year	This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.

Name	Provider / Domaine	Expiration	Description
_pk_id	InnoCraft Ltd .uliege.be	1 year	Used to store a few details about the user such as the unique visitor ID
_pk_ses	InnoCraft Ltd .uliege.be	30 minutes	Short lived cookies used to temporarily store data for the visit
_pk_ref	InnoCraft Ltd .uliege.be	6 months	Used to store the attribution information, the referrer initially used to visit the website