One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation
This work addresses implementation challenges in locally private statistical surveys, offering a more practical solution for real-world deployment, though it appears incremental as it builds on existing LDP QMLE methods.
The paper tackles the impracticalities of existing locally private quasi-maximum likelihood estimators (LDP QMLE) by proposing an alternative protocol that avoids long waiting times, high communication costs, and restrictive assumptions, making it more deployable for large-scale surveys, while providing theoretical guarantees like consistency and asymptotic normality.
Local differential privacy~(LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator~(QMLE) has been developed, but the existing method to build LDP QMLE is difficult to implement for a large-scale survey system in the real world due to long waiting time, expensive communication cost, and the boundedness assumption of derivative of a log-likelihood function. We provided an alternative LDP protocol without those issues, which is potentially much easily deployable to a large-scale survey. We also provided sufficient conditions for the consistency and asymptotic normality and limitations of our protocol. Our protocol is less burdensome for the users, and the theoretical guarantees cover more realistic cases than those for the existing method.