Asymptotically Optimal Bayes and Minimax Procedures in Sequential Estimation

Asymptotically Pointwise Optimal Procedures in Sequential Analysis

Asymptotically minimax Bayes predictive densities

fθ log (fθ/f̂) is used to examine various ways of choosing prior distributions; the principal type of choice studied is minimax. We seek asymptotically least favorable predictive densities for which the corresponding asymptotic risk is minimax. A result resembling Stein’s paradox for estimating normal means by the maximum likelihood holds for the uniform prior in the multivariate location family...

Optimal sequential procedures with Bayes decision rules

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the...

Minimax Optimal Procedures for Locally Private Estimation

Working under a model of privacy in which data remains private even from the statistician,we study the tradeoff between privacy guarantees and the risk of the resulting statistical estima-tors. We develop private versions of classical information-theoretic bounds, in particular thosedue to Le Cam, Fano, and Assouad. These inequalities allow for a precise characterization ofs...

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 int...