On the stationary distribution of iterative imputations

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

Research output: Contribution to journalArticlepeer-review

Abstract

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
JournalBiometrika
Volume101
Issue number1
DOIs
StatePublished - Mar 2014

Keywords

  • Chained equation
  • Convergence
  • Iterative imputation
  • Markov chain

ASJC Scopus subject areas

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

Fingerprint

Dive into the research topics of 'On the stationary distribution of iterative imputations'. Together they form a unique fingerprint.

Cite this