Functional stability of one-step GM-estimators in approximately linear regression

This paper provides a comparative sensitivity analysis of one-step Newton-Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analy...

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Autores principales: Simpson, D.G., Yohai, V.J.
Formato: JOUR
Materias:
Breakdown point
Maximum bias function
Newton-Raphson
Robust statistics
Weighted least squares
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00905364_v26_n3_p1147_Simpson
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00905364_v26_n3_p1147_Simpson2023-10-03T14:54:40Z Functional stability of one-step GM-estimators in approximately linear regression Simpson, D.G. Yohai, V.J. Breakdown point Maximum bias function Newton-Raphson Robust statistics Weighted least squares This paper provides a comparative sensitivity analysis of one-step Newton-Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by ε-contamination of the model. These bounds yield breakdown points and local rates of convergence of the bias as ε decreases to zero. We treat a unified class of Newton-Raphson estimators, including one-step versions of the well-known Schweppe, Mallows and Hill-Ryan GM estimators. Of the three well-known types, the Hill-Ryan form emerges as the most stable in terms of one-step estimation. The Schweppe form is susceptible to a breakdown of the Hessian matrix. For this reason it fails to improve on the local stability of the initial estimator, and it may lead to falsely optimistic estimates of precision. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00905364_v26_n3_p1147_Simpson
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Breakdown point
Maximum bias function
Newton-Raphson
Robust statistics
Weighted least squares
spellingShingle Breakdown point
Maximum bias function
Newton-Raphson
Robust statistics
Weighted least squares
Simpson, D.G.
Yohai, V.J.
Functional stability of one-step GM-estimators in approximately linear regression
topic_facet Breakdown point
Maximum bias function
Newton-Raphson
Robust statistics
Weighted least squares
description This paper provides a comparative sensitivity analysis of one-step Newton-Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by ε-contamination of the model. These bounds yield breakdown points and local rates of convergence of the bias as ε decreases to zero. We treat a unified class of Newton-Raphson estimators, including one-step versions of the well-known Schweppe, Mallows and Hill-Ryan GM estimators. Of the three well-known types, the Hill-Ryan form emerges as the most stable in terms of one-step estimation. The Schweppe form is susceptible to a breakdown of the Hessian matrix. For this reason it fails to improve on the local stability of the initial estimator, and it may lead to falsely optimistic estimates of precision.
format JOUR
author Simpson, D.G.
Yohai, V.J.
author_facet Simpson, D.G.
Yohai, V.J.
author_sort Simpson, D.G.
title Functional stability of one-step GM-estimators in approximately linear regression
title_short Functional stability of one-step GM-estimators in approximately linear regression
title_full Functional stability of one-step GM-estimators in approximately linear regression
title_fullStr Functional stability of one-step GM-estimators in approximately linear regression
title_full_unstemmed Functional stability of one-step GM-estimators in approximately linear regression
title_sort functional stability of one-step gm-estimators in approximately linear regression
url http://hdl.handle.net/20.500.12110/paper_00905364_v26_n3_p1147_Simpson
work_keys_str_mv AT simpsondg functionalstabilityofonestepgmestimatorsinapproximatelylinearregression
AT yohaivj functionalstabilityofonestepgmestimatorsinapproximatelylinearregression
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