On the stationary distribution of iterative imputations

Jingchen Liu, Andrew Gelman, Jennifer Hill, Yu Sung Su, Jonathan Kropko

Research output: Contribution to journalArticlepeer-review


Iterative imputation, in which variables are imputed one at a time conditional on all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modelling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties, accounting for the conditional models being iteratively estimated from data rather than being prespecified. When the families of conditional models are compatible, we provide sufficient conditions under which the imputation distribution converges in total variation to the posterior distribution of a Bayesian model. When the conditional models are incompatible but valid, we show that the combined imputation estimator is consistent.

Original languageEnglish (US)
Pages (from-to)155-173
Number of pages19
Issue number1
StatePublished - Mar 2014


  • Chained equation
  • Convergence
  • Iterative imputation
  • Markov chain

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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