International Statistical Review

Proper and Improper Multiple Imputation

Soren Feodor Nielsen

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Abstract

Multiple imputation has become viewed as a general solution to missing data problems in statistics. However, in order to lead to consistent asymptotically normal estimators, correct variance estimators and valid tests, the imputations must be proper. So far it seems that only Bayesian multiple imputation, i.e.\ using a Bayesian predictive distribution to generate the imputations, or approximately Bayesian multiple imputations has been shown to lead to proper imputations in some settings. In this paper, we shall see that Bayesian multiple imputation does not generally lead to proper multiple imputations. Furthermore, it will be argued that for general statistical use, Bayesian multiple imputation is inefficient even when it is proper.

Article information

Source
Internat. Statist. Rev., Volume 71, Number 3 (2003), 593-607.

Dates
First available in Project Euclid: 21 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.isr/1066768710

Zentralblatt MATH identifier
1114.62323

Keywords
Missing data Multiple imputation Congeniality Efficiency

Citation

Feodor Nielsen, Soren. Proper and Improper Multiple Imputation. Internat. Statist. Rev. 71 (2003), no. 3, 593--607. https://projecteuclid.org/euclid.isr/1066768710


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References

  • [1] \bibitem{Gelman} Gelman, A. (1996). Inference and monitoring convergence. In {\em Markov chain Monte Carlo in practice}, Eds. W.R. Gilks, S. Richardson & D.J. Spiegelhalter. Chapman & Hall.
  • [2] \bibitem{Heitjan and Rubin} Heitjan, D.F. & Rubin, D.B. (1991). Ignorability and coarse data. {\em Ann. Statist.}, 19, 2244-2253.
  • [3] \bibitem{Meng} Meng, X.-L. (1994). Multiple-imputation inferences with uncongenial sources of input. {\em Statist. Sci.}, 9, 538-558.
  • [4] \bibitem{Nielsen} Nielsen, S.F. (2000). Relative coarsening at random. {\em Statist. Neerlandica}, 54, 79-99.
  • [5] \bibitem{Robins and Wang} Robins, J.M. & Wang, N. (2000). Inference for imputation estimators. {\em Biometrika}, 87, 113-124.
  • [6] \bibitem{Rubin} Rubin, D.B. (1987). {\em Multiple Imputation for Nonresponse in Surveys}. Wiley.
  • [7] \bibitem{Rubin} Rubin, D.B. (1996). Multiple imputation after 18+ years. {\em J. Amer. Statist. Assoc.}, 91, 473-489.
  • [8] \bibitem{Schafer} Schafer, J. (1997). {\em Analysis of Incomplete Multivariate Data}. Chapman & Hall.
  • [9] \bibitem{Schenker and Welsh} Schenker, N. & Welsh, A.H. (1988). Asymptotic results for multiple imputation. {\em Ann. Statist.}, 16, 1550-1566.
  • [10] van der Vaart, A.W. (1998). {\em Asymptotic Statistics}. Cambridge University Press.
  • [11] \bibitem{Wang and Robins} Wang, N. & Robins, J.M. (1998). Large-sample theory for parametric multiple imputation procedures. {\em Biometrika}, 85, 935-948.