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A Bootstrap Method for a Multiple-Imputation Variance Estimator in Survey Sampling

Author

Listed:
  • Lili Yu

    (Department of Biostatistics, Epidemiology and Environmental Health Sciences, JPH College of Public Health, Georgia Southern University, Statesboro, GA 30460, USA)

  • Yichuan Zhao

    (Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA)

Abstract

Rubin’s variance estimator of the multiple imputation estimator for a domain mean is not asymptotically unbiased. Kim et al. derived the closed-form bias for Rubin’s variance estimator. In addition, they proposed an asymptotically unbiased variance estimator for the multiple imputation estimator when the imputed values can be written as a linear function of the observed values. However, this needs the assumption that the covariance of the imputed values in the same imputed dataset is twice that in the different imputed datasets. In this study, we proposed a bootstrap variance estimator that does not need this assumption. Both theoretical argument and simulation studies show that it was unbiased and asymptotically valid. The new method was applied to the Hox pupil popularity data for illustration.

Suggested Citation

  • Lili Yu & Yichuan Zhao, 2022. "A Bootstrap Method for a Multiple-Imputation Variance Estimator in Survey Sampling," Stats, MDPI, vol. 5(4), pages 1-11, November.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:74-1241:d:988071
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    References listed on IDEAS

    as
    1. S Chen & D Haziza & C Léger & Z Mashreghi, 2019. "Pseudo-population bootstrap methods for imputed survey data," Biometrika, Biometrika Trust, vol. 106(2), pages 369-384.
    2. Jae Kwang Kim & J. Michael Brick & Wayne A. Fuller & Graham Kalton, 2006. "On the bias of the multiple‐imputation variance estimator in survey sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 509-521, June.
    3. Jae Kwang Kim & J. N. K. Rao, 2009. "A unified approach to linearization variance estimation from survey data after imputation for item nonresponse," Biometrika, Biometrika Trust, vol. 96(4), pages 917-932.
    4. Adam Davey & Michael J. Shanahan & Joseph L. Schafer, 2001. "Correcting for Selective Nonresponse in the National Longitudinal Survey of Youth Using Multiple Imputation," Journal of Human Resources, University of Wisconsin Press, vol. 36(3), pages 500-519.
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