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

Ana M. Bianco (), Graciela Boente (), Wenceslao González-Manteiga () and Ana Pérez-González ()
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Ana M. Bianco: Universidad de Buenos Aires and CONICET Ciudad Universitaria
Graciela Boente: Universidad de Buenos Aires and IMAS, CONICET Ciudad Universitaria
Wenceslao González-Manteiga: Universidad de Santiago de Compostela
Ana Pérez-González: Universidad de Vigo

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 1, No 9, 106-146

Abstract: 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 $$\alpha $$ α -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.

Keywords: Fisher consistency; Kernel weights; L-estimators; Marginal functionals; Missing at random; Semiparametric models; 62F10; 62G08 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11749-018-0591-5

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