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Optimal pseudolikelihood estimation in the analysis of multivariate missing data with nonignorable nonresponse

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  • Jiwei Zhao
  • Yanyuan Ma

Abstract

SUMMARYTang et al. (2003) considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first, Tang et al. (2003) only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that in Tang et al. (2003).

Suggested Citation

  • Jiwei Zhao & Yanyuan Ma, 2018. "Optimal pseudolikelihood estimation in the analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 105(2), pages 479-486.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:2:p:479-486.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy007
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    Citations

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    Cited by:

    1. Li, Mengyan & Ma, Yanyuan & Zhao, Jiwei, 2022. "Efficient estimation in a partially specified nonignorable propensity score model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    2. Rui Duan & C. Jason Liang & Pamela Shaw & Cheng Yong Tang & Yong Chen, 2020. "Missing at Random or Not: A Semiparametric Testing Approach," Papers 2003.11181, arXiv.org.
    3. Aiai Yu & Yujie Zhong & Xingdong Feng & Ying Wei, 2023. "Quantile regression for nonignorable missing data with its application of analyzing electronic medical records," Biometrics, The International Biometric Society, vol. 79(3), pages 2036-2049, September.

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