On the stationary distribution of iterative imputations

• 成果类型: Article
• 署名作者: Liu, Jingchen; Gelman, Andrew; Hill, Jennifer; Su, Yu-Sung; Kropko, Jonathan
• 署名单位: Columbia University; New York University; Tsinghua University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast044
• 发表日期: 2014
• 页码: 155173
• 关键词: multiple-imputation; convergence-rates

摘要

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.