Asymptotic in a class of network models with an increasing sub-Gamma degree sequence

For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with 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.