This paper aims to construct a valid and efficient confidence interval for the extrema of parameters under privacy protection. The usual statistical inference on the extrema of parameters often suffers from the selection bias issue, and the problem becomes more acute, as in many application scenarios of extrema parameters, we often need to protect the privacy of the data. In this paper, we focus on the exponential family of distributions and propose a privatized parametric bootstrap method to address selection bias in the extrema of parameters problem under the scheme of differential privacy. While the usual privatized parametric bootstrap does not address selection bias appropriately, we prove that with a privatized bias correction term, the proposed parametric bootstrap method can lead to a valid and efficient confidence interval for the extrema of parameters. We illustrate the proposed method with the Gaussian case and regression case and demonstrate the advantages of the proposed method via numerical experiments.
翻译:本文旨在为受隐私保护的参数的极限构建一个有效和有效的信任间隔。通常对参数极限的统计推论往往因选择偏差问题而受到影响,而问题变得更为尖锐,正如在许多应用极端参数的情景中一样,我们常常需要保护数据的隐私。在本论文中,我们侧重于分布的指数式组合,并提议一种私有化的参数陷阱方法,以解决在差异隐私办法下的参数极限的选择偏差。虽然通常的私有化参数陷阱没有适当地解决选择偏差问题,但我们证明,如果采用私有化的偏差修正术语,拟议的参数边际靴套件方法可以导致对参数极限的有效和有效信任间隔。我们用数字实验来说明高斯案例和回归案例的拟议方法,并展示拟议方法的优势。</s>