Asymptotic Inferences in Synthesized Microdata via Multiple Imputation

• Activity Number: 665
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Government Statistics
• Author(s): Fang Liu*+ and Kaifeng Lu
• Companies: University of Notre Dame and Forest Labs
• Keywords: Statistical disclosure control (limitation) ; full synthesis ; partial synthesis ; selective multiple imputation of keys (SMIKe)

Abstract

Sensitive information in microdata can be effectively protected by replacing full or a portion of original data with values synthesized via multiple imputation (MI). Point estimators are defined as the averages of individual estimates from each of the $m$ released data sets. In this talk, we present a general large-sample framework providing the $sqrt(n)$-consistency and asymptotic normality of the point estimators. In particular, asymptotic distributions will be provided for cases where synthesis models are based on full or partial original data. We will also show that the regular empirical variance estimator $W+(1+1/m)B$ as used in the missing data setting overestimates the asymptotic variance of the point estimates. Our results are consistent with some previous work done in a Bayesian context.