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Comparison of Tests and Confidence Intervals for Univariate Normal Mean Based on Multiply Imputed Synthetic Data Obtained by Posterior Predictive Sampling
Comparison of Tests and Confidence Intervals for Univariate Normal Mean Based on Multiply Imputed Synthetic Data Obtained by Posterior Predictive Sampling
RRS2024-06
Abstract
There is a huge literature on data analysis under privacy or confidentiality protection. Among many inferential statistical methods based on parametric models, data analysis based on perturbation of original sensitive data using plug-in and posterior predictive sampling are quite common. In this paper we consider a very basic inferential problem of tests and confidence intervals for a normal mean with unknown variance based on synthetic data obtained from multiple imputations under posterior predictive sampling method. Several methods are suggested and compared. A general expression of the local power of a class of tests is also derived which can be used in a design context to determine a combination of sample size and number of imputations to guarantee a desired level of local power. A measure of privacy protection is derived to demonstrate that privacy would be compromised if too many imputations are released. An application to draw inference about the household earnings, corresponding to a US Census Bureau data, is illustrated.
Page Last Revised - September 5, 2024
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