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Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework

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  • Shu Yang
  • Jae Kwang Kim

Abstract

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator for finite‐population inference using a superpopulation model framework. We also clarify conditions for its robustness. For variance estimation, the conventional bootstrap inference is invalid for matching estimators with a fixed number of matches due to the nonsmoothness nature of the matching estimator. We propose a new replication variance estimator, which is asymptotically valid. The key strategy is to construct replicates directly based on the linear terms of the martingale representation for the matching estimator, instead of individual records of variables. Simulation studies confirm that the proposed method provides valid inference.

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  • Shu Yang & Jae Kwang Kim, 2020. "Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 839-861, September.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:3:p:839-861
    DOI: 10.1111/sjos.12429
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    Cited by:

    1. Shu Yang & Yunshu Zhang, 2023. "Multiply robust matching estimators of average and quantile treatment effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 235-265, March.
    2. Chenyin Gao & Katherine Jenny Thompson & Jae Kwang Kim & Shu Yang, 2022. "Nearest neighbour ratio imputation with incomplete multinomial outcome in survey sampling," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1903-1930, October.
    3. Jae Kwang Kim & Seho Park & Yilin Chen & Changbao Wu, 2021. "Combining non‐probability and probability survey samples through mass imputation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 941-963, July.

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