High breakdown-point estimates of regression by means of the minimization of an efficient scale

A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously the following properties: (a) they are qualitatively robust, (b) their breakdown point is .5, and (c) they are highly efficient for regression models with normal errors. They are defined by minimizing a ne...

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Detalles Bibliográficos
Publicado: 1988
Materias:
Bias robustness
High efficiency
Robust estimate
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v83_n402_p406_Yohai
http://hdl.handle.net/20.500.12110/paper_01621459_v83_n402_p406_Yohai
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01621459_v83_n402_p406_Yohai
record_format dspace
spelling paper:paper_01621459_v83_n402_p406_Yohai2023-06-08T15:13:39Z High breakdown-point estimates of regression by means of the minimization of an efficient scale Bias robustness High efficiency Robust estimate A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously the following properties: (a) they are qualitatively robust, (b) their breakdown point is .5, and (c) they are highly efficient for regression models with normal errors. They are defined by minimizing a new scale estimate, τ, applied to the residuals. Asymptotically, a τ estimate is equivalent to an M estimate with a ψ function given by a weighted average of two ψ functions, one corresponding to a very robust estimate and the other to a highly efficient estimate. The weights are adaptive and depend on the underlying error distribution. We prove consistency and asymptotic normality and give a convergent iterative computing algorithm. Finally, we compare the biases produced by gross error contamination in the τ estimates and optimal bounded-influence estimates. © 1976 Taylor & Francis Group, LLC. 1988 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v83_n402_p406_Yohai http://hdl.handle.net/20.500.12110/paper_01621459_v83_n402_p406_Yohai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bias robustness
High efficiency
Robust estimate
spellingShingle Bias robustness
High efficiency
Robust estimate
High breakdown-point estimates of regression by means of the minimization of an efficient scale
topic_facet Bias robustness
High efficiency
Robust estimate
description A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously the following properties: (a) they are qualitatively robust, (b) their breakdown point is .5, and (c) they are highly efficient for regression models with normal errors. They are defined by minimizing a new scale estimate, τ, applied to the residuals. Asymptotically, a τ estimate is equivalent to an M estimate with a ψ function given by a weighted average of two ψ functions, one corresponding to a very robust estimate and the other to a highly efficient estimate. The weights are adaptive and depend on the underlying error distribution. We prove consistency and asymptotic normality and give a convergent iterative computing algorithm. Finally, we compare the biases produced by gross error contamination in the τ estimates and optimal bounded-influence estimates. © 1976 Taylor & Francis Group, LLC.
title High breakdown-point estimates of regression by means of the minimization of an efficient scale
title_short High breakdown-point estimates of regression by means of the minimization of an efficient scale
title_full High breakdown-point estimates of regression by means of the minimization of an efficient scale
title_fullStr High breakdown-point estimates of regression by means of the minimization of an efficient scale
title_full_unstemmed High breakdown-point estimates of regression by means of the minimization of an efficient scale
title_sort high breakdown-point estimates of regression by means of the minimization of an efficient scale
publishDate 1988
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v83_n402_p406_Yohai
http://hdl.handle.net/20.500.12110/paper_01621459_v83_n402_p406_Yohai
_version_ 1768541603949969408

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