robust estimation; influence function; logistic regression; maximum likelihood
Abstract :
[en] A fast and stable algorithm to compute a highly robust estimator for the logistic regression model is proposed. A criterium. for the existence of this estimator at finite samples is derived and the problem of the selection of an appropriate loss function is discussed. It is shown that the loss function can be chosen such that the robust estimator exists if and only if the maximum likelihood estimator exists. The advantages of using a weighted version of this estimator are also considered. Simulations and an example give further support for the good performance of the implemented estimators. (C) 2003 Elsevier B.V. All rights reserved.
Disciplines :
Mathematics Computer science
Author, co-author :
Croux, C.
Haesbroeck, Gentiane ; Université de Liège - ULiège > Département de mathématique > Statistique (aspects théoriques)
Language :
English
Title :
Implementing the Bianco and Yohai estimator for logistic regression
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
Albert A. Anderson J.A. On the existence of maximum likelihood estimates in logistic regression models Biometrika 71 1984 1-10
Atkinson A. Riani M. Robust Diagnostic Regression Analysis 2000 Springer New York
Bianco A.M. Yohai V.J. Robust estimation in the logistic regression model Rieder H. Robust Statistics, Data Analysis, and Computer Intensive Methods Lecture Notes in Statistics Vol. 109 1996 17-34 Springer New York
Brent R. Algorithms for Minimization without Derivatives 1973 Prentice-Hall Englewood Cliffs, NJ, USA
Cantoni E. Ronchetti E. Robust inference for generalized linear models J. Amer. Statist. Assoc. 96 2001 1022-1030
Carroll R.J. Pederson S. On robust estimation in the logistic regression model J. Roy. Statist. Soc. B 55 1993 693-706
Christmann A. Rousseeuw P.J. Measuring overlap in binary regression Comp. Statist. Data Anal. 37 2001 65-75
Croux C. Haesbroeck G. Influence function and efficiency of the minimum covariance determinant scatter matrix estimator J. Multivariate Anal. 71 1999 161-190
Croux C. Flandre C. Haesbroeck G. The breakdown behavior of the maximum likelihood estimator in the logistic regression model Statist. Probab. Lett. 60 2002 377-386
Finney D.J. The estimation from individual records of the relationship between dose and quantal response Biometrika 34 1947 320-334
Hampel F.R. Ronchetti E.M. Rousseeuw P.J. Stahel W.A. Robust Statistics: The Approach based on Influence Functions 1986 Wiley New York
Kordzakhia N. Mishra G.D. Reiersølmoen L. Robust estimation in the logistic regression model J. Statist. Planning Inference 98 2001 211-223
Künsch H.R. Stefanski L.A. Carroll R.J. Conditionally unbiased bounded influence estimation in general regression models, with applications to generalized linear models J. Amer. Statist. Assoc. 84 1989 460-466
Pregibon D. Resistant fits for some commonly used logistic models with medical applications Biometrics 38 1982 485-498
Rousseeuw, P.J., 1985. Multivariate estimation with high breakdown point. In: Grossmann, W., Pflug, G., Vincze, I., Wertz, W. (Ed.), Mathematical Statistics and Applications, Vol. B. Reidel, Dordrecht, pp. 283-297.
Rousseeuw, P.J., Christmann, A., 2002. Robustness against separation and outliers in logistic regression. Comput. Statist. Data Anal. to appear.
Rousseeuw P.J. Van Driessen K. A fast algorithm for the minimum covariance determinant estimator Technometrics 41 1999 212-223
Rousseeuw P.J. van Zomeren B.C. Unmasking multivariate outliers and leverage points J. Amer. Statist. Assoc. 85 1990 633-639
Santner T.J. Duffy D.E. A note on A. Albert and J.A. Anderson's conditions for the existence of maximum likelihood estimates in logistic regression Biometrika 73 1986 755-758
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
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.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
