Empirical likelihood inference in general linear model with missing values in response and covariates by MNAR mechanism

  • Fayyaz Bahari
  • Safar ParsiEmail author
  • Mojtaba Ganjali
Regular Article


In this paper, we utilize a general linear model for analyzing data with missing values in some covariates and response variable. Our aim is to fit a general linear model and to construct a confidence region for the parameters of the general linear model based on the empirical likelihood ratio function. Also, we assume that missing data may happen in covariates or in response variable or in both of them with missing not at random mechanism where the probability of missing a datum is specified by a logistic model. We use inverse probability weights and an augmented method as the auxiliary condition of empirical likelihood to estimate parameters of the general linear model. Asymptotic properties of the empirical log-likelihood ratio are investigated whether the exponential tilting parameter is known or estimated by the follow-up sample. The asymptotic normality of estimators is also proved. Some simulation studies are used to illustrate the performance of our model for different sample sizes. Also, a real dataset is studied by the proposed methods.


General linear model Missing data Exponential tilting Augmented method Inverse probability weights method Empirical log-likelihood ratio 



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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesUniversity of Mohaghegh ArdabilArdabilIran
  2. 2.Department of Statistics, Faculty of Mathematical SciencesShahid Beheshti UniversityTehranIran

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