Although the asymptotic properties of the parameter estimator have been derived in the $p_{0}$ model for directed graphs with the differentially private bi-degree sequence, asymptotic theory in general models is still lacking. In this paper, we release the bi-degree sequence of directed graphs via the discrete Laplace mechanism, which satisfies differential privacy. We use the moment method to estimate the unknown model parameter. We establish a unified asymptotic result, in which consistency and asymptotic normality of the differentially private estimator holds. We apply the unified theoretical result to the Probit model. Simulations and a real data demonstrate our theoretical findings.

翻译：虽然参数估量器的无光度特性已产生于 $p ⁇ 0}$美元模型中,用于使用有差异的私人双度序列的定向图形,但一般模型中仍然缺乏无光度理论。在本文中,我们通过离散 Laplace 机制发布定向图形的双度序列,该机制满足了不同隐私。我们使用这一瞬时方法来估计未知的模型参数。我们建立了一个统一的无光度结果,在这个结果中,差异的私人估量器具有一致性和无光度常态。我们对Probit 模型应用了统一的理论结果。模拟和真实数据展示了我们的理论结论。