🤖 AI Summary
This study addresses the challenge of performing efficient and robust statistical inference for target parameters—such as causal effects—under local differential privacy constraints. We propose a novel integration of the rate-double-robust inference framework with local privacy mechanisms, where noise is injected into individual-level data to ensure privacy protection. Leveraging semiparametric theory, our approach successfully transfers desirable properties of non-private estimators to the privatized setting. The resulting method guarantees unbiasedness and achieves semiparametric efficiency, while also preserving the original estimator’s convergence rate under privacy perturbations. Furthermore, it maintains favorable asymptotic performance under both nonparametric and parametric perturbation regimes, demonstrating broad applicability and robustness in practical privacy-preserving inference tasks.
📝 Abstract
We reconcile privacy protection and rate-double-robust inference. The privacy of individuals is protected by a local privacy mechanism: injecting noise into their sensitive data, revealing only the noisy data for inference. Hence, privacy protection hinders inference. In contrast, the inference of a target parameter is rate-double-robust when the large-sample bias of an estimator of the parameter is characterised by a trade-off between the estimation errors of two other, nuisance, parameters. Hence, rate-double-robustness facilitates inference. Our starting point of reconciliation is a class of rate-double-robust target parameters indexed linearly by an infinite-dimensional and nonlinearly by a low-dimensional regression. Among others, this includes causal parameters. To infer these targets privately, we show how suitable privacy mechanisms transfer the semiparametric properties of the sensitive-data model to the private setting. Rate-double-robustness is transferred, enabling locally-private, unbiased and semiparametrically efficient inference of our target parameters. Finally, we transform general nonparametric nuisance estimators into private ones, which inherit convergence properties of their nonprivate counterparts. For parametric nuisance models, we develop a private method-of-moments estimator and its large-sample inference theory.