Local privacy and statistical minimax rates

We study the tradeoff between privacy guarantees and the utility of statistical estimators under local differential privacy, where data remains private even from the statistician. We prove bounds on information-theoretic quantities that influence estimation rates as a function of the amount of privacy preserved. Our bounds can be viewed as quantitative data-processing inequalities that, combined with minimax techniques such as Le Cam's and Fano's methods, allow for precise characterization of statistical rates under local privacy constraints.