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Pseudo likelihood‐based estimation and testing of missingness mechanism function in nonignorable missing data problems

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  • Xuerong Chen
  • Guoqing Diao
  • Jing Qin

Abstract

In nonignorable missing response problems, we study a semiparametric model with unspecified missingness mechanism model and a exponential family model for response conditional density. Even though existing methods are available to estimate the parameters in exponential family, estimation or testing of the missingness mechanism model nonparametrically remains to be an open problem. By defining a “synthesis" density involving the unknown missingness mechanism model and the known baseline “carrier" density in the exponential family model, we treat this “synthesis" density as a legitimate one with biased sampling version. We develop maximum pseudo likelihood estimation procedures and the resultant estimators are consistent and asymptotically normal. Since the “synthesis" cumulative distribution is a functional of the missingness mechanism model and the known carrier density, proposed method can be used to test the correctness of the missingness mechanism model nonparametrically andindirectly. Simulation studies and real example demonstrate the proposed methods perform very well.

Suggested Citation

  • Xuerong Chen & Guoqing Diao & Jing Qin, 2020. "Pseudo likelihood‐based estimation and testing of missingness mechanism function in nonignorable missing data problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1377-1400, December.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:4:p:1377-1400
    DOI: 10.1111/sjos.12493
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    References listed on IDEAS

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    1. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.

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