We examine privacy-preserving inferences of group mean differences in zero-inflated right-skewed (zirs) data. Zero inflation and right skewness are typical characteristics of ads clicks and purchases data collected from e-commerce and social media platforms, where we also want to preserve user privacy to ensure that individual data is protected. In this work, we develop likelihood-based and model-free approaches to analyzing zirs data with formal privacy guarantees. We first apply partitioning and censoring (PAC) to ``regularize'' zirs data to get the PAC data. We expect inferences based on PAC to have better inferential properties and more robust privacy considerations compared to analyzing the raw data directly. We conduct theoretical analysis to establish the MSE consistency of the privacy-preserving estimators from the proposed approaches based on the PAC data and examine the rate of convergence in the number of partitions and privacy loss parameters. The theoretical results also suggest that it is the sampling error of PAC data rather than the sanitization error that is the limiting factor in the convergence rate. We conduct extensive simulation studies to compare the inferential utility of the proposed approach for different types of zirs data, sample size and partition size combinations, censoring scenarios, mean differences, privacy budgets, and privacy loss composition schemes. We also apply the methods to obtain privacy-preserving inference for the group mean difference in a real digital ads click-through data set. Based on the theoretical and empirical results, we make recommendations regarding the usage of these methods in practice.

翻译：我们研究了零膨胀右偏态(zirs)数据中组均值差异的隐私保护推断问题。零膨胀与右偏态是电子商务和社交媒体平台收集的广告点击与购买数据的典型特征，同时我们需要保护用户隐私以确保个体数据安全。本文提出了基于似然法和无模型方法，在严格隐私保证下分析zirs数据。首先通过分区与删失(PAC)对zirs数据进行"正则化"处理得到PAC数据。相较于直接分析原始数据，基于PAC的推断具有更优的推断性质和更稳健的隐私考量。我们进行理论分析，建立了基于PAC数据的隐私保护估计量的MSE一致性，并考察了其关于分区数量和隐私损失参数的收敛速率。理论结果同时表明，限制收敛速率的因素是PAC数据的抽样误差而非脱敏误差。我们开展了广泛的模拟研究，比较了所提方法在不同类型zirs数据、样本量与分区规模组合、删失场景、均值差异、隐私预算及隐私损失组合方案下的推断效用。同时，我们将该方法应用于真实数字广告点击率数据集，实现了组均值差异的隐私保护推断。基于理论与实证结果，我们给出了这些方法在实际应用中的使用建议。