标题： 通过间接估计和参数 Bootstrap 进行隐私数据上的最优去偏推断 显示英文标题

标题： Optimal Debiased Inference on Privatized Data via Indirect Estimation and Parametric Bootstrap

摘要： 我们设计了一个去偏的参数引导框架，用于从差分隐私数据中进行统计推断。 在隐私数据上使用参数引导的现有方法忽略了或避免处理截断的影响，这是一种大多数隐私机制采用的技术。 忽略截断的影响通常会导致置信区间的覆盖不足以及假设检验的类型I误差校准错误。 现有方法失败的主要原因是基于隐私数据的参数估计不一致。 我们建议使用间接推断方法来一致地估计参数值，并在参数引导中使用改进的估计量进行推断。 为了实现间接估计量，我们提出了一种新颖的基于模拟的自适应方法，并提供了建立相应参数引导估计量、置信区间和假设检验一致性的理论。 特别是，我们证明了我们的自适应间接估计量在所有基于发布摘要统计量的“良好行为”一致估计量中达到了最小渐近方差。 我们的模拟研究显示，我们的框架生成的置信区间具有良好的覆盖率，并且假设检验的类型I误差正确，对于位置尺度正态分布、简单线性回归和逻辑回归的推断表现出最先进的性能。 显示英文摘要

摘要： We design a debiased parametric bootstrap framework for statistical inference from differentially private data. Existing usage of the parametric bootstrap on privatized data ignored or avoided handling the effect of clamping, a technique employed by the majority of privacy mechanisms. Ignoring the impact of clamping often leads to under-coverage of confidence intervals and miscalibrated type I errors of hypothesis tests. The main reason for the failure of the existing methods is the inconsistency of the parameter estimate based on the privatized data. We propose using the indirect inference method to estimate the parameter values consistently, and we use the improved estimator in parametric bootstrap for inference. To implement the indirect estimator, we present a novel simulation-based, adaptive approach along with the theory that establishes the consistency of the corresponding parametric bootstrap estimates, confidence intervals, and hypothesis tests. In particular, we prove that our adaptive indirect estimator achieves the minimum asymptotic variance among all "well-behaved" consistent estimators based on the released summary statistic. Our simulation studies show that our framework produces confidence intervals with well-calibrated coverage and performs hypothesis testing with the correct type I error, giving state-of-the-art performance for inference on location-scale normals, simple linear regression, and logistic regression.