One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation

TL;DR

This paper introduces a practical one-bit local differential privacy protocol for quasi-MLE that is easier to implement at scale, providing theoretical guarantees on its asymptotic behavior and limitations.

Contribution

It proposes a simplified LDP quasi-MLE protocol that overcomes implementation challenges of existing methods, with proven asymptotic normality and broader applicability.

Findings

The protocol is easier to deploy in large-scale surveys.

It guarantees asymptotic normality under realistic conditions.

It identifies limitations of the proposed method.

Abstract

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.