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We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially private algorithms to estimate confidence intervals. Crucially, our algorithms guarantee a finite sample coverage, as opposed to an asymptotic coverage. Unlike most previous differentially private algorithms, we do not require the domain of the samples to be bounded. We also prove lower bounds on the expected size of any differentially private confidence set showing that our the parameters are optimal up to polylogarithmic factors.
One of the most common statistical goals is to estimate a population parameter and quantify uncertainty by constructing a confidence interval. However, the field of differential privacy lacks easy-to-use and general methods for doing so. We partially
We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. T
Consider a two-treatment, two-period crossover trial, with responses that are continuous random variables. We find a large-sample frequentist 1-alpha confidence interval for the treatment difference that utilizes the uncertain prior information that there is no differential carryover effect.
$f$-DP has recently been proposed as a generalization of classical definitions of differential privacy allowing a lossless analysis of composition, post-processing, and privacy amplification via subsampling. In the setting of $f$-DP, we propose the c
We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe $U$ of items, possibly of infinite size, and a database $D$ of users. Each user $i$ contributes a subset $W_i subseteq U$