Discussion on “ Minimax Optimal Procedures for Locally Private Estimation ”

We congratulate Professors Duchi, Jordan and Wainwright on their path-breaking work in statistical decision theory and privacy. Their extension of classical information-theoretic lower bounds of Le Cam, Fano, and Assouad to local differential privacy can potentially lead to a systematic study of various lower bounds under all kinds of privacy constraints. Their successful treatments of some interesting problems in the paper shed light on possibly a unified theory for a general statistical framework.