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A unified empirical likelihood approach for testing MCAR and subsequent estimation

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  • Shixiao Zhang
  • Peisong Han
  • Changbao Wu

Abstract

For an estimation with missing data, a crucial step is to determine if the data are missing completely at random (MCAR), in which case a complete‐case analysis would suffice. Most existing tests for MCAR do not provide a method for a subsequent estimation once the MCAR is rejected. In the setting of estimating means, we propose a unified approach for testing MCAR and the subsequent estimation. Upon rejecting MCAR, the same set of weights used for testing can then be used for estimation. The resulting estimators are consistent if the missingness of each response variable depends only on a set of fully observed auxiliary variables and the true outcome regression model is among the user‐specified functions for deriving the weights. The proposed method is based on the calibration idea from survey sampling literature and the empirical likelihood theory.

Suggested Citation

  • Shixiao Zhang & Peisong Han & Changbao Wu, 2019. "A unified empirical likelihood approach for testing MCAR and subsequent estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 272-288, March.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:1:p:272-288
    DOI: 10.1111/sjos.12351
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    Cited by:

    1. Hairu Wang & Zhiping Lu & Yukun Liu, 2023. "Score test for missing at random or not under logistic missingness models," Biometrics, The International Biometric Society, vol. 79(2), pages 1268-1279, June.

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