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Empirical likelihood method for non-ignorable missing data problems

Author

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  • Zhong Guan

    (Indiana University South Bend)

  • Jing Qin

    (National Institute of Allergy and Infectious Diseases)

Abstract

Missing response problem is ubiquitous in survey sampling, medical, social science and epidemiology studies. It is well known that non-ignorable missing is the most difficult missing data problem where the missing of a response depends on its own value. In statistical literature, unlike the ignorable missing data problem, not many papers on non-ignorable missing data are available except for the full parametric model based approach. In this paper we study a semiparametric model for non-ignorable missing data in which the missing probability is known up to some parameters, but the underlying distributions are not specified. By employing Owen (1988)’s empirical likelihood method we can obtain the constrained maximum empirical likelihood estimators of the parameters in the missing probability and the mean response which are shown to be asymptotically normal. Moreover the likelihood ratio statistic can be used to test whether the missing of the responses is non-ignorable or completely at random. The theoretical results are confirmed by a simulation study. As an illustration, the analysis of a real AIDS trial data shows that the missing of CD4 counts around two years are non-ignorable and the sample mean based on observed data only is biased.

Suggested Citation

  • Zhong Guan & Jing Qin, 2017. "Empirical likelihood method for non-ignorable missing data problems," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 113-135, January.
    • Handle: RePEc:spr:lifeda:v:23:y:2017:i:1:d:10.1007_s10985-016-9381-0
    DOI: 10.1007/s10985-016-9381-0
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    References listed on IDEAS

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    Cited by:

    1. Tianqing Liu & Xiaohui Yuan, 2020. "Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data," Statistical Papers, Springer, vol. 61(6), pages 2241-2270, December.
    2. Sima Sharghi & Kevin Stoll & Wei Ning, 2024. "Statistical inferences for missing response problems based on modified empirical likelihood," Statistical Papers, Springer, vol. 65(7), pages 4079-4120, September.

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