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

Author

Listed:
  • Fayyaz Bahari

    (University of Mohaghegh Ardabil)

  • Safar Parsi

    (University of Mohaghegh Ardabil)

  • Mojtaba Ganjali

    (Shahid Beheshti University)

Abstract

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.

Suggested Citation

  • Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Empirical likelihood inference in general linear model with missing values in response and covariates by MNAR mechanism," Statistical Papers, Springer, vol. 62(2), pages 591-622, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01103-0
    DOI: 10.1007/s00362-019-01103-0
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    References listed on IDEAS

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    5. Zhao, Hui & Zhao, Pu-Ying & Tang, Nian-Sheng, 2013. "Empirical likelihood inference for mean functionals with nonignorably missing response data," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 101-116.
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