Asymptotic in a class of network models with an increasing sub-Gamma degree sequence
This provides theoretical guarantees for privacy-preserving network analysis, though it appears incremental as an extension of existing differential privacy mechanisms to network models.
The authors derived asymptotic properties for parameter estimators in binary network models with differentially private degree sequences under sub-Gamma noise, establishing consistency and asymptotic normality as parameters increase to infinity.
For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.