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Empirical likelihood inference for mean functionals with nonignorably missing response data

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  • Zhao, Hui
  • Zhao, Pu-Ying
  • Tang, Nian-Sheng

Abstract

An empirical likelihood (EL) approach to inference on mean functionals with nonignorably missing response data is developed. The nonignorably missing mechanism is specified by an exponential tilting model. Several maximum EL estimators (MELEs) for the response mean functional are proposed under different scenarios. We systematically investigate asymptotic properties of the proposed MELEs for the response mean functional. With the use of auxiliary information, MELEs are statistically more efficient. Confidence intervals (CIs) for the response mean are constructed on the basis of the EL method and the normal approximation (NA) method. Simulation studies are presented to evaluate the finite sample performance of our proposed MELEs and CIs. A real earnings data from the New York Social Indicators Survey is used to illustrate our proposed EL method. Empirical results show that our proposed EL method is robust.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:66:y:2013:i:c:p:101-116
    DOI: 10.1016/j.csda.2013.03.023
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    References listed on IDEAS

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    1. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
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    5. Kim, Jae Kwang & Yu, Cindy Long, 2011. "A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 157-165.
    6. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.
    7. Liugen Xue, 2009. "Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 671-685, December.
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    Cited by:

    1. 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.
    2. Hong-Xia Xu & Guo-Liang Fan & Han-Ying Liang, 2017. "Hypothesis test on response mean with inequality constraints under data missing when covariables are present," Statistical Papers, Springer, vol. 58(1), pages 53-75, March.
    3. Zhang, Yan-Qing & Tang, Nian-Sheng, 2017. "Bayesian local influence analysis of general estimating equations with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 184-200.
    4. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    5. Deng, Jianqiu & Yang, Xiaojie & Wang, Qihua, 2022. "Surrogate space based dimension reduction for nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    6. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Goodness of fit test for general linear model with nonignorable missing on response variable," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 163-196, March.
    7. Guo, Xu & Song, Lianlian & Fang, Yun & Zhu, Lixing, 2019. "Model checking for general linear regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 1-12.

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