Continuity and differentiability of regression M functionals

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This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A restricted type of differentiability, called weak differenti...

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Autores principales: Maronna, Ricardo Antonio, Sued, Mariela
Publicado: 2012
Materias:
Asymptotic normality
Consistency
MM estimates
Nonlinear regression
S estimates
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13507265_v18_n4_p1284_Fasano
http://hdl.handle.net/20.500.12110/paper_13507265_v18_n4_p1284_Fasano
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_13507265_v18_n4_p1284_Fasano
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spelling paper:paper_13507265_v18_n4_p1284_Fasano2023-06-08T16:10:54Z Continuity and differentiability of regression M functionals Maronna, Ricardo Antonio Sued, Mariela Asymptotic normality Consistency MM estimates Nonlinear regression S estimates This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A restricted type of differentiability, called weak differentiability, is defined, which suffices to prove the asymptotic normality of estimates based on the functionals. This approach allows to prove the consistency, asymptotic normality and qualitative robustness of M estimates under more general conditions than those required in standard approaches. In particular, we prove that regression MMestimates are asymptotically normal when the observations are φ-mixing. © 2012 ISI/BS. Fil:Maronna, R.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sued, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13507265_v18_n4_p1284_Fasano http://hdl.handle.net/20.500.12110/paper_13507265_v18_n4_p1284_Fasano
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic normality
Consistency
MM estimates
Nonlinear regression
S estimates
spellingShingle Asymptotic normality
Consistency
MM estimates
Nonlinear regression
S estimates
Maronna, Ricardo Antonio
Sued, Mariela
Continuity and differentiability of regression M functionals
topic_facet Asymptotic normality
Consistency
MM estimates
Nonlinear regression
S estimates
description This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A restricted type of differentiability, called weak differentiability, is defined, which suffices to prove the asymptotic normality of estimates based on the functionals. This approach allows to prove the consistency, asymptotic normality and qualitative robustness of M estimates under more general conditions than those required in standard approaches. In particular, we prove that regression MMestimates are asymptotically normal when the observations are φ-mixing. © 2012 ISI/BS.
author Maronna, Ricardo Antonio
Sued, Mariela
author_facet Maronna, Ricardo Antonio
Sued, Mariela
author_sort Maronna, Ricardo Antonio
title Continuity and differentiability of regression M functionals
title_short Continuity and differentiability of regression M functionals
title_full Continuity and differentiability of regression M functionals
title_fullStr Continuity and differentiability of regression M functionals
title_full_unstemmed Continuity and differentiability of regression M functionals
title_sort continuity and differentiability of regression m functionals
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13507265_v18_n4_p1284_Fasano
http://hdl.handle.net/20.500.12110/paper_13507265_v18_n4_p1284_Fasano
work_keys_str_mv AT maronnaricardoantonio continuityanddifferentiabilityofregressionmfunctionals
AT suedmariela continuityanddifferentiabilityofregressionmfunctionals
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