One goal of statistical privacy research is to construct a data release
mechanism that protects individual privacy while preserving information
content. An example is a {\em random mechanism} that takes an input database
$X$ and outputs a random database $Z$ according to a distribution
$Q_n(\cdot|X)$. {\em Differential privacy} is a particular privacy requirement
developed by computer scientists in which $Q_n(\cdot |X)$ is required to be
insensitive to changes in one data point in $X$. This makes it difficult to
infer from $Z$ whether a given individual is in the original database $X$. We
consider differential privacy from a statistical perspective. We consider
several data release mechanisms that satisfy the differential privacy
requirement. We show that it is useful to compare these schemes by computing
the rate of convergence of distributions and densities constructed from the
released data. We study a general privacy method, called the exponential
mechanism, introduced by McSherry and Talwar (2007). We show that the accuracy
of this method is intimately linked to the rate at which the probability that
the empirical distribution concentrates in a small ball around the true
distribution.

研究统计隐私的目标之一是构建一个数据发布机制，它可以在保护个人隐私的同时保留信息内容。本文从统计角度考虑差分隐私，研究满足差分隐私要求的数据发布机制，并比较它们的收敛速度。研究表明，指数机制的准确性与经验分布在真实分布周围集中的概率密切相关。