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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2013
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03195724_v41_n1_p111_Sued http://hdl.handle.net/20.500.12110/paper_03195724_v41_n1_p111_Sued |
| Aporte de: |
| Sumario: | 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. |
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