Robust location estimation with missing data

In a missing data setting, we have a sample in which a vector of explanatory variables xi is observed for every subject i, while scalar responses yi are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at ran...

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Autores principales: Sued, M., Yohai, V.J.
Formato: JOUR
Materias:
Asymptotic distribution
Breakdown point
L-location functional
M-location functional
Median
Missing at random
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03195724_v41_n1_p111_Sued
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_03195724_v41_n1_p111_Sued
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spelling todo:paper_03195724_v41_n1_p111_Sued2023-10-03T15:23:14Z Robust location estimation with missing data Sued, M. Yohai, V.J. Asymptotic distribution Breakdown point L-location functional M-location functional Median Missing at random In a missing data setting, we have a sample in which a vector of explanatory variables xi is observed for every subject i, while scalar responses yi are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L-functionals and M-functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. © 2012 Statistical Society of Canada. Fil:Sued, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03195724_v41_n1_p111_Sued
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 distribution
Breakdown point
L-location functional
M-location functional
Median
Missing at random
spellingShingle Asymptotic distribution
Breakdown point
L-location functional
M-location functional
Median
Missing at random
Sued, M.
Yohai, V.J.
Robust location estimation with missing data
topic_facet Asymptotic distribution
Breakdown point
L-location functional
M-location functional
Median
Missing at random
description In a missing data setting, we have a sample in which a vector of explanatory variables xi is observed for every subject i, while scalar responses yi are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L-functionals and M-functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. © 2012 Statistical Society of Canada.
format JOUR
author Sued, M.
Yohai, V.J.
author_facet Sued, M.
Yohai, V.J.
author_sort Sued, M.
title Robust location estimation with missing data
title_short Robust location estimation with missing data
title_full Robust location estimation with missing data
title_fullStr Robust location estimation with missing data
title_full_unstemmed Robust location estimation with missing data
title_sort robust location estimation with missing data
url http://hdl.handle.net/20.500.12110/paper_03195724_v41_n1_p111_Sued
work_keys_str_mv AT suedm robustlocationestimationwithmissingdata
AT yohaivj robustlocationestimationwithmissingdata
_version_ 1807323057854873600

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