Differentially Private Hypothesis Testing For Normal Random Variables.
Open Access
- Author:
- Solea, Eftychia
- Graduate Program:
- Statistics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- None
- Committee Members:
- Aleksandra B Slavkovic, Thesis Advisor/Co-Advisor
- Keywords:
- differential privacy
hypothesis testing
normal distribution - Abstract:
- Data privacy has become a fundamental problem in statistical data analysis. Consider a database that contains sensitive information. The goal of private data analysis is to publish valid statistical results without compromising the privacy of the individuals whose data are stored in the dataset. In this thesis, we design private algorithms with rigorous privacy guarantees. The formal privacy notion we use is differential privacy which has received significant attention because it offers meaningful guarantees of privacy in the presence of any external or auxiliary of information. Differential privacy guarantees that no more information can be extracted about an individual from the statistical database than what is already available in the presence of any external information. This is critical in fields that handle sensitive data, such as medical data, financial data and personal data from social networking sites. In our work, we design differentially private estimators for statistical inference. We focus on normal distribution and we compare the performance of the differentially private estimators with the classical maximum likelihood estimator. We also propose approximate sample size adjustment factors needed for sample size calculation in classical hypothesis testing to achieve certain power and Type I error. Finally, we illustrate the effect of privacy on Type I and Type II error rates for two statistical hypothesis procedures subject to differential privacy.