Generation and Analysis of Synthetic Data for Privacy Protection Under the Multivariate Linear Regression Model

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Mathematics and Statistics



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In this dissertations, the author derives likelihood-based exact inference for multiply imputed synthetic data under the multiple (p>1) univariate linear regression model and for singly and multiply imputed data under the multivariate linear regression model. In the former, the synthetic data are generated under plug-in sampling, where unknown parameters in the model are set equal to observed values of point estimators. In the latter, synthetic data are also generated under posterior predictive sampling where they are drawn from a posterior predictive distribution. Simulations are presented to confirm the methodology performs as the theory predicts and to evaluate privacy protection. Robustness studies are also given. In the final chapter, a new privacy protection method similar to bottom- and top-coding is proposed and its inferential properties explored.