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Plug-in marginal estimation under a general regression model with missing responses and covariates

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Abstract

In this paper, we consider a general regression model where missing data occur in the response and in the covariates. Our aim is to estimate the marginal distribution function and a marginal functional, such as the mean, the median or any \(\alpha \)-quantile of the response variable. A missing at random condition is assumed in order to prevent from bias in the estimation of the marginal measures under a non-ignorable missing mechanism. We give two different approaches for the estimation of the responses distribution function and of a given marginal functional, involving inverse probability weighting and the convolution of the distribution function of the observed residuals and that of the observed estimated regression function. Through a Monte Carlo study and two real data sets, we illustrate the behaviour of our proposals.

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Acknowledgements

The authors wish to thank two anonymous referees for valuable comments which led to an improved version of the original paper. This work was partially developed while Ana M. Bianco and Graciela Boente were visiting the Departamento de Estatística, Análise Matemática e Optimización de la Universidad de Santiago de Compostela, Spain under the bilateral agreement between the Universidad de Buenos Aires and the Universidad de Santiago de Compostela. This research was partially supported by Grants pict 2014-0351 from anpcyt and 20020130100279BA from the Universidad de Buenos Aires, Argentina and also by the Spanish Projects MTM2013-41383P and MTM2016-76969P from the Ministry of Science and Innovation, Spain. A. Bianco and G. Boente also wish to thank the Minerva Foundation for its support to present some of this paper results at the International Conference on Robust Statistics 2017.

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Authors and Affiliations

  1. Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET Ciudad Universitaria, Pabellón 2, 1428, Buenos Aires, Argentina

    Ana M. Bianco

  2. Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina

    Graciela Boente

  3. Departamento de Estatística, Análise Matemática e Optimización, Facultad de Matemáticas, Universidad de Santiago de Compostela, Campus Sur., 15706, Santiago de Compostela, Spain

    Wenceslao González-Manteiga

  4. Departamento de Estadística e Investigación Operativa, Universidad de Vigo, Campus Orense. Campus Universitario As Lagoas s/n, 32004, Ourense, Spain

    Ana Pérez-González

Authors
  1. Ana M. Bianco
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  2. Graciela Boente
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  3. Wenceslao González-Manteiga
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  4. Ana Pérez-González
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Corresponding author

Correspondence to Graciela Boente.

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Bianco, A.M., Boente, G., González-Manteiga, W. et al. Plug-in marginal estimation under a general regression model with missing responses and covariates. TEST 28, 106–146 (2019). https://doi.org/10.1007/s11749-018-0591-5

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