In the case of the differential privacy under the Laplace mechanism, the asymptotic properties of parameter estimators have been derived in some special network models with common binary values, but the asymptotic properties in network models with the ordered values are lacking. In this paper, the authors release the degree sequences of the ordered networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. The authors establish the asymptotic result including the consistency and asymptotical normality of the parameter estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.

在拉普拉斯机制下的差分隐私情况下，在一些具有共同二进制值的特殊网络模型中已经推导出参数估计量的渐近性质，但缺乏具有有序值的网络模型的渐近性质。在本文中，作者以离散拉普拉斯机制为特例，在一般噪声机制下发布有序网络的度数序列。作者建立了参数估计量趋于无穷大时参数估计量的一致性和渐近正态性的渐近结果。提供了模拟和真实数据示例来说明渐近结果。