Privacy-preserving Inference of Group Mean Difference in Zero-inflated Right Skewed Data with Partitioning and Censoring

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.