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

Ana M. Bianco ^[1] ; Graciela Boente ^[1] ; Wenceslao González-Manteiga ^[2] ; Ana Pérez-González ^[3]
1. [1] Universidad de Buenos Aires
  
  Universidad de Buenos Aires
  
  Argentina
2. [2] Universidade de Santiago de Compostela
  
  Universidade de Santiago de Compostela
  
  Santiago de Compostela, España
3. [3] Universidade de Vigo
  
  Universidade de Vigo
  
  Vigo, España
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Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 1, 2019, págs. 106-146
Idioma: inglés
DOI: 10.1007/s11749-018-0591-5
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Resumen
- 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 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.