Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | Robust location estimation with missing data |
Autor: | Sued, M.; Yohai, V.J. |
Filiación: | Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, University of Buenos Aires and CONICET, Buenos Aires, Argentina Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, University of Buenos Aires and CONICET, Buenos Aires, Argentina
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Palabras clave: | Asymptotic distribution; Breakdown point; L-location functional; M-location functional; Median; Missing at random |
Año: | 2013
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Volumen: | 41
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Número: | 1
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Página de inicio: | 111
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Página de fin: | 132
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DOI: |
http://dx.doi.org/10.1002/cjs.11163 |
Título revista: | Canadian Journal of Statistics
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Título revista abreviado: | Can. J. Stat.
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ISSN: | 03195724
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03195724_v41_n1_p111_Sued |
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Citas:
---------- APA ----------
Sued, M. & Yohai, V.J.
(2013)
. Robust location estimation with missing data. Canadian Journal of Statistics, 41(1), 111-132.
http://dx.doi.org/10.1002/cjs.11163---------- CHICAGO ----------
Sued, M., Yohai, V.J.
"Robust location estimation with missing data"
. Canadian Journal of Statistics 41, no. 1
(2013) : 111-132.
http://dx.doi.org/10.1002/cjs.11163---------- MLA ----------
Sued, M., Yohai, V.J.
"Robust location estimation with missing data"
. Canadian Journal of Statistics, vol. 41, no. 1, 2013, pp. 111-132.
http://dx.doi.org/10.1002/cjs.11163---------- VANCOUVER ----------
Sued, M., Yohai, V.J. Robust location estimation with missing data. Can. J. Stat. 2013;41(1):111-132.
http://dx.doi.org/10.1002/cjs.11163