Date of Award
2022
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Statistics
First Advisor
T. Tony Cai
Abstract
This dissertation studies the trade-off between differential privacy and statistical accuracy in parameter estimation problems. We understand the privacy-accuracy trade-off by finding the best achievable accuracy of any differentially private algorithm, also known as the "privacy-constrained minimax risk", in a series of statistical problems: Gaussian mean estimation and linear regression, estimation in general parametric models, and non-parametric function estimation. The increasing difficulty and generality of this series is matched by the development of differentially private algorithms such as noisy iterative hard thresholding, and of minimax lower bound techniques such as the score attack.
Recommended Citation
Wang, Yichen, "Topics In Differentially Private Statistical Inference" (2022). Publicly Accessible Penn Dissertations. 5529.
https://repository.upenn.edu/edissertations/5529