Likelihood-Based Finite Sample Inference for Synthetic Data from a Multiple Linear Regression Model

• Activity Number: 462
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Government Statistics Section
• Author(s): Martin Klein*+
• Companies: U.S. Census Bureau
• Keywords: Maximum likelihood estimator ; Pivot ; Plug-in sampling ; Posterior predictive sampling ; Statistical disclosure control

Abstract

Likelihood-based finite sample inference based on synthetic data is developed in this paper under a multiple linear regression model. We consider two distinct synthetic data generation scenarios, one based on posterior predictive sampling, and the other based on plug-in sampling where unknown parameters are set equal to the observed value of their point estimators. We demonstrate that valid inference can be drawn in both scenarios, even for a singly imputed synthetic dataset; and we show that plug-in sampling will generally lead to more efficient inference than posterior predictive sampling. We discuss the usual combination rules for drawing inference under multiple synthetic datasets in the context of likelihood-based data analysis.